I currently have F1 single entry visa. I want to know is it possible I could not get visa to come back to US?

They are not obligated to give a new visa, you need to meet the requirements each time you apply.

If he in fact stated he was a U.S. citizen he is permanently inadmissible.

Expired work authorization

Not really, you are authorized to work until the application is approved.

I'm a US citizen married to a retired Frenchman. What about Visa and Medicare for him if we live in the USA?

He is ineligible for medicare and all other means tested, federal public benefits until he becomes a US citizen. Moreover, you are responsible if...

H1 transfer outside US

If you never entered the U.S. to work for employer A, you cannot enter on the visa for employer B to work for employer A.

H1b RFE Response Mailing Deadline

Overnight courier on August 11th, or by hand on August 12th. U.S. mail, there is no way to know how long it will take.

Applied for n400 and they been investigating my case

If you are separated, you cannot get the N-400 approved. Under the regulations, you have to be together still.

Deadline to apply for H1B and the L1 Visa this year?When is the next call for applications for both?The total fees to issue them

If he works for you now, L1 is a possibility. If he has a bachelor's degree and you have a job requiring his degree, you can file an H1b petition...

Generally one need not be admitted to the Illinois bar to practice immigration law, particularly if they are simply coming to Illinois to go to court.

If his income is sufficient right now, it should be fine. If you are authorized to work, your income can also be included.