How to determine numerical values/quantitiy of cards in a card game?

The reason why you can't find much about the answers is. These questions are asked AFTER you have thought of a game.
You first need to create a game where the other rules and mechanics are known. And during the design, the first answers will simply pop up in your head.

If I where to relate to my game (where I like to do something ridiculous compared to other games):

1) Since all players share one deck, 120 cards.

2a) Since the first rounds are more of a build up, and the cards are only a small addition to the game. 0 cards to start with.

2b) It's a strategy; 1 player might take monopoly on all 120 cards eventually. Now, you might wonder where they are placed when played. Well, back into the deck actually.

3) This is a tough question and one that you can ask when designing the specific card. I got it linked to how much a card weighs in influence on the game. I am using 6 as the main number. This for 1 type. If a card is only 50%, I am allowing myself to use 12 cards of these. However, if they are from the same type, I only allow 1 type. Thus 3 of 100% and 6 of 50% would make the total set of that type.

As you can see, I am answering the questions. Based on some knowledge of my own game.
We can't really answer the question for you. Only you know your game.
Of course, if you designed your game. And you are still unsure. You could return with the question after explaining the game and showing the cards that you thought of.

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If you want to design a card game with the numbers thought of before hand. Than a generic answer would be:

1) 40/player. 60 if some rounds, multiple cards can be picked.
2a) 7

2b) 7

3) 4

1) This is something you will need to calculate...and it may take some planning. My card game specifically has 50 cards in each deck, so that buying sleeves isn't a hassle (sleeves are bought in 50 sleeve increments). Fantasy Flight's (FFG) Warhammer 40k Conquest has a limit at 50, but each deck has its warlord (1 card not included in deck count), the warlord's 8 cronies (which brings it down to 42), and the rest that have restrictions. There's a 3 card limit of any one card per deck, so it makes it easy for you to build a deck of 14 sets of 3. FFG's Star Wars LCG has 10/50 in a deck comprised of: 10 objective cards; each objective cards has 5 linked cards that must be in the deck...so 10 objectives with 5 cards linked to each objective = 50 cards. It makes deck building simpler than other games.

Basically you need to set a number. Typically Magic: The Gathering (MTG) uses 60 minimum and for most card games, it typically works. However, MTG allows for higher numbers, which tweaks the chances a particular card can appear in a game. FFG usually uses 50 in all their card games.

It's what you want it to be, but you have to also have to: Set card limits (2, 3, 4, more, or just 1 copy of any one card in a deck) and allow for player strategy (the more a card appears in a deck, the higher chances they will get that card in a given game). You will need to set those rules while you are figuring out how many cards you need in your decks.

2) This is another thing you will need to set, but figure out in play testing. It basically comes down to how many options do you want player to have. This is compounded by things like: How many cards you draw in a given turn, how are you going to chain card combos, How you're going to set up your resource system, and how it's going to impact gameplay. You'll have to really scrutinize when your play testers devise their strategies. Try 1 card higher in one game and 1 card lower in another. Try extremes.

3) Like I said in #1, You will need to determine how many copies of a particular card will appear, then play test it. Typically, you'll base it on card potential. If the card could be overpowered, make it a limit of 1. If it's a utility card that isn't a game changer (but heavy in theme), you may want to have 3 or 4. One thing is for certain, you will need to graphically be able to show how many of that card can be in a deck. It's hard because you want each card to balance itself (i.e. a powerful ability needs to cost more or take more time to bring out), but some cards will end up being favored and you'll understand that in play testing...that's the only way. When you see that, you start making restrictions or allowances. It's a weird balance cause you can either nerf or buff a particular card, or you can change the instances it can appear in a deck. In my game, I had a card that basically nullified 1 incoming attack...that's all. I had set the instances of a card in my decks at 2, but in play testing, I found that games were going hours...and I wanted to be an hour maximum. After more testing I found it was that particular card that was the culprit. While the ability itself wasn't that powerful, it exponentially prolonged games when both players knew how to use them. So instead of nerf'ing the ability, I only had 1 instance of that card in both decks. The result was that game times were literally cut in half. That's what I needed, but I only figured it out after TONS of gameplay.

Basically...set the numbers yourself, play test the crap out of it because you can't mathematically determine how your engine works against human players, then make changes accordingly. It's a tedious process, but that's what works. The more complicated the mechanic, the more play testing needed. This is why bigger companies like BushiRoad, Wizards of the Coast, and Fantasy Flight Games can effectively release card games that are consistently good; they have the manpower to test out all the mechanics.

But let's crunch some numbers...

If you have just 10 cards in a deck, with a possible 10 results (unique cards) in any single slot (permutations)...you'll have over 3 million combinations of those 10 cards. Imagine the combinations with 50 cards...

MTG...60 card deck can have any combination of over 15,000 cards (cards released without reprints from the beginning until now) and a maximum of 4 of any one card in a deck...now you can see how immensely crazy their job is.

Let's face it, many people want to create their own card game, but there's so much more that goes into it than just creating cards. There's theme, mechanics, balance, tons of forethought, and an immense amount of game testing. Even with my game...a 2 player card game with 50-card static (no customization available) decks, it took months of play testing...going to conventions, showing my game to game designers, critics, strangers, my students, and the like...to even think that my game is balanced. Now that I've got a solid base to stand on, I can grow my brand, but I understand that it will take a lot more play testing because now I have to consider my expansions against my original set.