1 - Embedded questions use statement word order.
Did Joe sell his car?
I wonder if Joe sold his car.
2 - Might and would are modals. Use one modal, not two.
I wonder what their reasons might have been.
Your grammar book certainly covers these topics. If you don't have a grammar book, English Grammar in Use by Murphy is famous. Paper copies are cheap and a google search will find a PDF. See units 29 and 50.