Am i still eligible for greencard?

no, your VAWA was based on the abuse, and your new marriage is not an issue.

Is it ok for me to file for greencard for my husband who has DACA. He entered on someone else's passport.

not necessarily, your naturalization will be ok as long as you did not help him with his entry scenario.

Which should be the first date I left the U.S. in the form N-400 regarding the section "Time outside the U.S."?

you can not shorten the time you spent outside of the US. you must state the actual date you left.

How can I fix my immigration status?

you may be able to apply for DACA, and you may be able to apply as your siblings did, but more information is needed to see what other relief may...

If a judge ordered joint custody will the father have to keep paying child support

they are two separate issues, talk to your divorce attorney representing you.

I am a graduate student on F1 status from Nepal. I am planning to apply for TPS but not EAD card to maintain my F1 status.

yes, you can apply for OPT after your graduation.

I am a US Citizen. My husband wants to apply for citizenship now. Will my juvenile record come up or affect his case?

your last 5 years history will be relevant but CIS can go beyond that to see if you meet the good moral character requirement. see an attorney.

How long USCIS will take to reply on L1B RFE? It's been more than 3 months. (Regular processing) Does it mean rejected?

120 days is about the average time it takes, be patient.

Do I need a family lawyer

no, you may be able to have the judge to adjust your obligation, seek a family law attorney.

there is no restriction for you to work in China.