Not recommended. If you have identification with different names, you could have all kinds of problems getting into the country, getting your...

It is correct that you can enter the U.S. ten days before the H1b status begins, and not more than that.

You don't need to transfer anything. The visas are in the same category and the embassy or consulate will enter the code when they issue the visa.

You are responsible that she not become a public charge until she becomes a U.S. citizen or has 40 quarters of income.

You need to file an i-290B motion to reopen and reconsider. Or refile.

You did not abandon status but you did interrupt your continuity. So four years and six months from the date you resumed your status is the earliest.

You don't need to file for her H4 extension. She can file it herself. And she can also file to change to any other immigration status for which...

If she files to extend or change her status, yes.

Check the category, and if you are in one of the approved categories you can work with the EAD receipt.

You can apply for a name change where you live in the U.S. if you wish.