Damage tables or just d6 variations? for dark fantasy game...

And also what are some ways I could handle elemental strengths/weaknesses in this type of system?

I'm aware of the bellcurve of 2d6 and how 7 is the most likely result, so I do appreciate 2d6 for that.
Though I do get your point about how d6 may be too random, I did playtest my idea of having armour d6 based and weapons 2d6 based and it gave a nice feel to the system and it made play quicker since one doesn't have to look up a table. I like the feel of stronger armour having a bit more of a chance of preventing damage but to the point where it's super powerful. This is a problem i've noticed in systems before that use armour as damage reduction instead of using as an AC type of system where armour affects the to hit roll, this site (read points 1-4) analyzes the issues that can come up with armour as DR:

http://www.seankreynolds.com/rpgfiles/rants/armorasdamagereduction.html

I think that by having armour based upon just d6 or variable in a way could remove those issues.

Btw, one mechanic in my game that will be there for combat in one form or another will be "bonus dice" , which is where you roll extra dice for what you're rolling for and you get to choose the highest results. So perhaps some really good armour (if it's d6 reduction based) could be like "1d6+1, 1b" which would mean you roll 2 dice, choose the highest and add +1 to the total for your total damage reduction provided.

"a Dice pool is something that can handle any character development and scaled infinitely, and can be easily given some additional functions by adding different colored dice to the pool (for elemental stuff and such)."

Indeed, that's why I was considering doing without the tables you roll on.

"Are you thinking of this game as deep and long lasting as something like D&D or something more easily picked up and played? If former, I think going through three tables in combat ain't that bad."
A mix. Each time you play the game though you start with a new character though, so any levelling up etc is done in one play session. There is some connections between each game you play, but not like having a character you keep from game to game. I guess you could say it's close to a "roguelike" or action game compared to a straight up full on traditional rpg.
Board games like Eldritch Horror and Mage Knight are sort of similar to how it'll be too with regard to character progression.

"but if you thought of having a lot of character development and upgrading it might not suffice."
You have 5 (or 6) attributes/stats in the game. The attributes show how good you are with things. They range from 1 (lowest) to 6 (highest). Starting attributes range from 1-3, and you can level them up by up to +2 each during the game (to get 6 you have to combine levelling up attributes with using some sort of attribute boosting gear or spells etc.).
One stat would be your Combat stat, which governs your physical melee/ranged skill. Once you get it high enough you get bonuses to your rolls with weapons etc...Bonuses for that would be "bonus dice" you get to roll with your weapon roll, instead of simply giving things like +x damage.
Thus, even though you do increase your character's stats, it isn't "a lot" of development of the character in a flat power increase. The game doesn't scale up infinitely with things like hp, weapon damage, etc...your character simply just gets more skilled with using what they acquire/have (e.g. more likely to get higher results when using weapons). This could work whether it's table based or using freeform dice as damage.

"Also, if you decide to stick with your first dice system, I think that the example table you provided should be something like (just to acknowledge snake eyes and double sixes):
Roll: 2/3-5/6-8/9-11/12
Damage: 0/2/3/3/6"

Since there is a "to hit" roll you need to do before you roll for damage I'd have it, if using table for damage, so that you can't get a "0" result for damage on the 2d6 roll for at least one of your damage types.

" If former, I think going through three tables in combat ain't that bad."
I found it to be pretty slow when I was playtesting it.
Keep in mind the three tables aren't separate. Consider a combat using the 2d6 table method. Here's how it'd play out:

First you roll to hit. You find what the target number needed on 2d6 to hit the opponent on by referencing your accuracy to their evasion on a table chart. Say, you have ACC 3 and they have EVA 3, so you have to roll 7+. You have a Combat bonus of +1B from your Combat stat. So you roll 3d6 and choose the 2 highest and if you roll 7+ you hit. (one aspect of the too hit part I didn't mention: you can get "surges" , which function as critical hits)

Say you hit them. So now you roll for damage on 2d6 and you reference the table to see what damage you do:

Roll: 2/3-5/6-8/9-11/12
Fire Sword Damage: Phys: 0/2/3/3/6
Mag: 0/0/0/0/0
Elem: 1/1/1/1/2

They then roll for their armour and shield:

Roll: 2/3-5/6-8/9-11/12
Blessed Plate Armour Reduction: Phys: 1/2/3/3/4
Mag: 1/1/2/2/3
Elem: 0/0/0/0/0
Leather Shield: 1d6 roll. 1-4: +0 DR. 5-6: +1 DR.

Say you rolled a 11. So you go 3 PHYS, 0 MAG, and 1 ELEM damage. and say they roll a 4 on their armour and 2 on their shield, for a total of 2 PHYS DR, 1 MAG DR, and 0 ELEM DR. So they take 2 damage in total.

It can take a bit of time to calculate all the damage and damage reduction from three sources like that I think. I could make the numbers bigger for damage and DR, but I'd to have it so that in the game things like daggers and weaker weapons would be viable and that the game wouldn't become just a chase to get the most outright powerful gear.

If armour DR is a bit more random (by using 1d6 base instead of 2d6 for its check) , then it could make the player decide whether it's worth it or not to wear it (wearing heavy armour would give you some sort of penalty in the game as well). Weaker weapons would have advantage of things like extra effects they cause other than damage, higher surge/crit rate etc...I don't want it to be so that weaker weapons HAVE to rely upon crits to hurt guys in strong armour. If I use the 2d6 chart method for armour, perhaps surges by weapons could reduce what you roll. so for example, a dagger's surge could make it so that you you roll on the chart but with only 1d6...

My main concern with the chart method is if it will slow down the game too much with math and be visually hard to reference. Rolling a dice and simply adding or subtracting or halving the result is a lot easier to do. In either system, I'm also still concerned/interested in finding a different way to simplify elemental strengths/weaknesses.

I am leaning towards using a system so it doesn't use tables for damage/DR, but I will keep in mind what you said about the possibility of 1d6 being too random for armour due to its range...

So, in summary, if it's tables it'd be like:

Roll: 2/3-5/6-8/9-11/12
Fire Sword Damage: Phys: 0/2/3/3/6
Mag: 0/0/0/0/0
Elem: 1/1/1/1/2

Roll: 2/3-5/6-8/9-11/12
Blessed Plate Armour Reduction: Phys: 1/2/3/3/4
Mag: 1/1/2/2/3
Elem: 0/0/0/0/0
Leather Shield: 1d6 roll. 1-4: +0 DR. 5-6: +1 DR.

if it's not tables it'd be like:

Fire Sword: 2d6+1 damage

Armour/shield roll (roll 2d6 and assign one die to shield, and one to armour to account for the shield being used to defend weak areas; or alternatively roll 2 dice of different colours one for shield one for armour)
Leather Armour: d3+2 DR
Large Shield: d6 roll: 1-3: 0DR, 4: 1 DR 5-6: 2DR

Although, thinking about it now, i could remove step 1 if I make it so you roll to hit only if enemy specifically "dodges" (i intend to have dodge, block, and parry as 3 separate things you can do, block is already covered by shield rules);
here's how it'd look:
he advantage of using tables though is that i could make some very exact ranges though
so with combat in summary it's like this:
1. Roll to hit. Target number is based on a comparison of your Accuracy vs their Evasion (acc and eva are determined by a number of factors), you consult a chart that shows Target Numbers based on a crossreference of ACC vs EVA and that give syou the number you must equal or beat on 2d6. if you hit , each individual 6 rolled counts as a "surge" and activates a special ability or effect of the weapon if you hit
smaller weapons do less damage but surge on 5s and 6s
2. roll to damage if you hit. by using code or chart
by using 2d6
3. defender rolls for damage reduction, 2d6, one dice is for armour, 1 for shield (whether using code or chart it still involves 2d6)
4. apply total damage left over as a reduction of HP
in step 3, medium and large shields have advantage of blocking more generally, but you must roll 2 separate coloured d6s. small shields block less but allow you to assign the dice as you want (thus allowing you to block better with your armour)
So blocking works by having a DR shield roll in step 3
parrying and dodge would be separate things
i could also remove step 1 and make it so you just roll to see if you surge, you only have to beat a target number if enemy specifically "dodges"

I think I may just keep with the idea that dodge makes it so you have to roll to hit rather than just seeing if your weapon surges.
I did consider having dodge make the opponent reroll their to hit roll, but if that were the case then it'd be very very hard to hit opponents that require a high target number to hit.
Btw, dodge, block, parry (defensive reactions) cost either an action point or energy point to use. EP are kind of a similar resource to magic points in most games. Action points you get a set amount each combat round , you use to attack and/or defend, you can get more defense by spending EPs.
I don't like your idea of parrying providing -1 to damage total (maybe to the to hit roll though may be fine) since that would make it so the opponent can never get a 12 on their damage roll (if using charts).
Not sure if I mentioned it earlier, but here's an idea I had for parry:
the opponent rolls to hit/check for surge. You can choose to parry after the roll if you are using a light shield like a buckler, but you must choose before the roll instead if you are using a medium shield like a kite shield. The opponent rolls to hit and then you roll to see if you parry by rolling 1d6+2 for small shields, 1d6+1 for medium. If you equal or exceed your opponent's total to hit/surge result then they end up missing (and perhaps you can perform an immediate counter attack). If you fail the parry they hit you and it counts as if they had got two surges even if they hadn't rolled the surges. The idea of parry is that it should be a high risk high reward type of thing with about (generally speaking) a 25% or so chance of success.
Block works by doing as I mentioned before.
Dodge , after having discussed this with you on here, I think could work in these different ways: 1. makes the opponent reroll their to hit, but costs 1 EP/AP 2. makes them have to do the to hit check and not just the surge check when rolling the 2d6 3. Maybe make it so it haves so that you have to EXCEED the target number for the to hit roll (if accuracy step always requires aiming for the target number) rather than simply being equal to or greater than it. 4. Make the to hit roll an opposed test.
Your evasion in the game btw would be based upon an agility stat, but limited by your armour. So you can wear heavy armour if you want but it will limit your max agility.
If I use your idea about there being no to hit roll and just the damage test, I'd change it so that surges occur on individual #s of 6s (or 5+s for certain weapons) rather than surges only occuring if you roll high. The idea of surges is that they add effects to your damage roll and/or boost the damage roll.
I also like how in the rough damage tables you posted, the dagger does more damage than the sword at the highest range. That's what I had in mind for weapons too. Some are more steady, whilst some have more varying ranges, etc.