May I use ground turkey for the meat?

Just be sure to use a ground turkey that has some fat- ie not those very lean ground turkey, you need the fat there to help develop and carry the flavor.
Note there are also several companies that make excellent meatless crumbles which are great for chili including trader joe’s, beyond meat, and boca brands

Also, you might shorten the cooking time just a bit

I don't see why not, although you won't get the flavor of pork or beef. It'd still be good, though; I think there's enough spices to carry the flavor banner here. Sometimes I use a dash of worcestershire sauce when cooking with ground turkey, just to add a little extra flavor