What should be our next step?

Marriage based adjustment of status to legal permanent residency will take care of all of your issues with employment authorization, residency etc....

Should I do anything to nullify the old incorrectly named contracts, or do I just need to do new ones with the correct co. name?

It appears that the "old" agreements are not valid because one party to the agreement has not signed it (you). You do run the hypothetical risk of...

Confused about what documents to bring

If you already submitted documents and the Service didn't ask for new ones then you don't need to prepare new ones. It would not be much of a...

Power of attorney is jurisdictional. i.e. It is only good where the transaction will be handled.

2- If we decide to franchise and expand to other states could this be an issue? Would trademarking name help us in any way?

In short, Yes it could be the issue; not probable but possible. If you will be doing good enough to franchise to another state/s then the expense...

Will this situation interfear with my ability to renew my green card?

It appears that you have temporary (2 year permanent resident card) permanent residency based on marriage to US citizen less than 2 years prior to...

You will be ok as long as you can explain your situation. In your circumstances hiring immigration attorney is probably a very good idea.

Address where you intend to reside as long as correspondence will not get lost.

Will my travel plan affect my pending H-1B application? Thank you very much for your answer

Yes it can affect negatively because by itself OPT is not a status.

Can I get ITIN if I have SSN ?

Unfortunately you will not be issued ITIN with SSN.