Can I lose my citizenship?

If you are not dishonorably discharged you will not lose it.

When can I remarry if I divorced in January 21 2019?

A min after your divorce is finalized. This is not a question of US immigration law. Seek counsel of a local family law attorney.

Can I quit my PhD program and go back to my previous H1B?

If you were approved subject to CAP initially, you still can reclaim the remainder of the six year period if properly petitioned for by a...

L1 to H1 transfer and extension of stay?

L1 stay period is counted towards the six yet limit on H1B.

It takes time for your physical file to be transferred to and then arrive in a new office.

No but you can neither seek change of status under INA 248 not an L visa at the consulate until you will have either complied with the INA 212(e)...

Take the record to a local immigration lawyer to look into it without A, B BBB, CCC and other abbreviations. Then ask for a substantive advice.

Joint sponsorship for form I-864?

"No, it is not necessary" would be a short answer to your question.

Could an LPR charged with abandonment of her status be eligible to file 212(k)?

Besides the points made by the colleague, INA 212k applies to very specific grounds of inadmissibility which DO NOT INCLUDE abandonment of LPR...

How can someone deported from US re enter?

One good way to explore his possibilities would be having a private consultation with a competent immigration lawyer. Bring his immigration record...