[ChuckF.]

If you have access to a table saw, I would make inside trim from 3/4"X 4" or so, with a big rabbet on the edge to accommodate that plastic fin on the window, coming out to be flush with the face of the drywall. Finish with standard trim molding.

 

[ChuckF.]

Re #4, I missed the fact that the bluish looking stuff is drywall. Remove the drywall, then trim as I described. Don't know if the rabbet will go inside that fin, or outside it without measuring.

Whoever did that should have put some shim material under the drywall so it was either tight under the fin, or butted into it, or covered it up. Any of those three would have been better.

 

[ChuckF.]

Drywall window trim vs wood trim is a matter of personal preference. I would remove the drywall and the plastic and put real wood in there, 3/4" in pine, fir or spruce, whatever you have in your part of the country.

Drywall window trim started as a way for builders to save money, because real wood moldings are getting expensive. Maybe drywall labor rates are less than finish carpenter rates. Some people might like them for their clean minimalist look. Maybe part of the reason I prefer wood trim is because I hate doing anything with drywall and like working with wood.

 

[ChuckF.]

You need shimming if you get the window down to bare 2x4's and you find it's been mounted off-center. You might also need it if the trim boards you use aren't thick enough to make it to the window frame. For this window it doesn't look like you will need it.

After you pull the drywall off, and the plastic thing, you should put some insulation into the space, either filler/rod and caulk, or loose-pack fiberglass, or foam in a can. Re caulk the crack, depends on color that you paint the wood, if it's not white, then caulk can mess up the transition.