Can I create Overwatch fan merchandise (such as prints, buttons, keychains, etc.) and sell it at conventions?
Legally, yes, if you get a license from Blizzard (unlikely, and if so, they'll probably want either money or a portion of your profits).
Otherwise, not legally. This is exactly the situation that IP law (e.g. copyright and trademark) was created to address. Blizzard created the game and so they have rights to control and benefit from derivatives there of. There are some exceptions, but prints, buttons, and keychains are not likely to meet the requirements for those.
No it is copy right protected.
You could draw a character of your own illustration of similar game settings with your own background and try to sell without logo.