This is a passive ability that is always active- it's just part of how he experiences the world and other people. I’m mashing mind reading and empathy into one because: Cole can sense/feel what others are feeling, and what he reads from their minds is often loosely based around what thoughts are attached to those feelings. Cole mainly hears thoughts and mental imagery that relate to the person feeling hurt, angry, scared, regret, etc.; Anything that he can potentially "help" or "fix," from unresolved deep-seated emotional wounds to minor inconveniences. In that sense it isn't quite the same as cut and dry traditional mind reading, or maybe on some level it could be- but Cole doesn't use it that way. If you ask him what number you're thinking of, he's more likely to recite your childhood trauma to you.

This ability also applies to physical locations, in that he can sense the residual strong emotions left behind in a specific place or location. With Cole, this often means reciting the last thoughts and feelings of those who died there. He can also read animals & plants, though they are generally much more simple in nature.

Also a passively active ability. This isn't true invisibility but more like the effect of a perception filter from Doctor Who; people just don't notice him even when he's in the same room, as if their mind doesn't want to see him and so chooses to simply not perceive him. He can technically extend this "invisibility" to at least one other person, but he's only done it one time in canon and it took a toll on him. While he can make himself visible to certain people or break the illusion by speaking, he is very easily forgotten once the encounter is over, and he can force someone to forget him if he chooses. It’s not clearly defined, but it seems that the more someone “wants” Cole to be real, or at least believes him to be, the easier it is to remember him (hence why the in-game party doesn’t constantly forget he exists). Cole may have some amount of control over that as well whether he does it consciously or not. But if he doesn’t exert his will one way or the other, then he will generally be forgotten in time. While he has limited control over it, this isn’t an ability he can completely “turn off” in his current state.

Spirit mediums or anyone with a related strong sensitivity/ability to communicate with spirits/the dead may not be affected by this, unless Cole consciously chooses to not be seen.

It’s been shown in canon that Cole has some ability to make others forget other older memories, though they may still have to relate to him in some way.

I won't go into the entire Rogue class mechanics especially since the accompanying skills are customizable to the player's liking, but in general he is skilled with double daggers and stealth. All rogues can also pick locks. His extra specialization is "Assassin" which involves about what you'd expect- attacking and killing quickly and silently. For specific in-game skills you can check out the Rogue class here and the Assassin specialization here.