I have a Warlock in my group who often wants to light things on fire, possess things, and do other improvised magical things. Should I make him do skill checks with his arcana or with his wisdom ability score? As far as I know, arcana is only used to get knowledge on magical subjects.
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That depends. A lot.
If it's something that he could do without magic that he's choosing to do that way for flavor, use whatever roll you would have used otherwise and describe it as magic. In cases where there wouldn't be one, just let it happen. He probably has a fire-based at-will anyway. Nothing was as onerous as the Fire-starting NWP in 2nd Ed. Failing to start a fire isn't interesting; at least not very often.
If it's something that has a significant impact or is outside the scope of the typical Warlock schtick (like possessing objects) then don't allow it. Much like Wizards are restricted by their spell books, Warlocks are restricted by their pacts. You can get around this a little bit with Wizard rituals but that's a Wizard Class Feature; not a Warlock one.
If you really insist on letting the Warlock do this or using a roll-for-magic approach it would definitely be Arcana. After all, what's going to help you cast magic better? Knowledge of magic or common sense? If you're going this route be prepared for the Fighter to start trying to cast rituals too, though. In 4th Edition, this actually makes about as much sense.