It’s not that bad, glue and screw. Remove the inner board from the drawer front and reattach it to the drawer first. You might have to clean up the MDF a bit. Use filler if you have to, maybe, but don’t use nails. Then reattach the drawer front - again with screws. It might not look perfect, but it’ll probably look fine when the drawer is closed. Consider wood block fillets at the interior corners (sacrificing a bit of space).

Alternatively you could rebuild the drawer frame, using the same drawer front so it matches.

No idea, we use the cheaper Kirkland brand - it works very well, don’t see a reason to pay more.

Our house has wall vents for all 4 bathrooms, so it’s definitely something allowed by code here. It works just fine, there are louvered exits on each one. It’s better than venting into the attic like a lot of older houses for sure.

You are going to love it. Gas is so much nicer to cook on, having flame control and immediate feedback. There’s nothing you really need to know, as such, you’ll figure it out quickly.