putting symbols on dice?

I have been working on a very fun PYL dice game unlike any I have seen before.

There are 16 dice all with a varying distribution of 4 possible outcomes. These are: treasure chests, doors, keys (that can either open chests or lock doors), and monsters.

Now the chest, door, and key symbols all remain constant. However, the monsters will look different based on their special ability. Note: If 3 monsters are in play at the same time, your turn ends.

So my question is, is it redundant or insulting to put a unifying "monster" icon such as a skull & crossbones in the top right for ALL monsters (ie. ghost/goblin/mimic, etc) so the player knows without a doubt that when they see 3 dice in play with "skull & crossbones" it ends their turn? Or should be be fairly obvious what is and isn't a monster compared to the standard chest/key/door?

Another question, how do you feel about icons that represent a monster's ability displayed on the die? (and obviously stated in a reference guide too)

Example: In my game, when a player locks a door using a key, any monsters currently in play are removed (thus resetting the number of monsters to 0). Ghosts have a special ability where they are NOT removed from play when a door is locked because they can float through them.

So, I can either;
a) explain this ability in the rules/reference and just have the ghost symbol on the dice with nothing else
b) explain this ability in the rules/reference and also display a "small door with an 'X' over it" icon next to the ghost symbol

The ghost's ability is pretty thematic and very easy to remember after one use so that example may not be the best but I am interested in everyone's thoughts.

Thank you for your time!