Windows are installed and no jambs present. They came with a 1/2 in. return on them for finishing and I have about an inch or so between the return and the buck. Which would be best material and approach to bring the extensions to finished wall area. I'd like to stay away from drywall eventhough there is abundant quantity of cut outs left . Any suggestions!

Really the choice is up to you. MDF if you're looking fora white extension. Finished wood if that's your thing.

What is the internal side of the window frames made of?

There is no inside to the window frame. Winows are magic windows. How would I finish the mdf in the corners of the extension, what is common pratice? Can mdf accept finishing nails, without cracking the edges, for the trim?

mdf should accept standard 18g. brads just fine, as long as you aren't putting them every inch for some wierd reason. If you are concerned you could go to a 21g. or 23g. brad nail(not headless)

I like using red oak plywood. It's not that much more than mdf and doesn't contain the formaldehyde, is denser and will be more durable.

Didn't realize this tread was still going so here's my closure.
First off the r/o was 1'' clearence all around frame so I had to fur out to the 1/2 " return on the frame.
Had more than enough scraps of drywall lying around to finish the countour with 1 full piece per side.

Steel corners to finish where the two drywall boards met. Several coats of waterproof pait especially on the bottow and we're done. Worst was taping inside corners! Still have the garage window to finish so might experience with
another product, not sure which one yet.
This was definetly the cheapest route! When the wife does get tired of it
I'll easily be able to finish over, rip it out, put some other finish and add a trim.
Cheers!