Can i file the I-130 petition for my J-1 husband who has already been in his home country for more than i year?

You need to consult with experience immigration attorney now. But the answer is yes.

Can I travel to US if I have h1 visa valid for 30 days on the day I travel?

It would be best to have the extension done and get the stamp and all, but if your situation does not allow that be sure to have proof of filing...

My asylum result

It would be impossible to guess, however, you need to contact the asylum office in writing and follow up with your case by hiring immigration lawyer.

Can I marry my fiance if he is cited as a dependent on his parent's asylum petition?

It is best in your situation to seek the advise of a competent immigration attorney. I am not sure that you are a US citizen or how your fiance...

As long as you meet the poverty guideline you should be fine. If you have proof from social security office that you have completed your 40 quarter...

Can I petition for my husband's immigrant visa while I am on medicaid? I will have a co-sponsor.

Yes, you may file an immigrant petition for your spouse so long as your or your combine income meets the poverty guideline.

How do I re-establish domicile in the US?

I am not sure as a citizen why you were denied? You need to consult with a lawyer..

How long will take normally to change visa from B-1 to F-1 for tow students which they are 16 & 23 years old.

Because they did not apply through consulate for F-1, now you have to show that they will return to their home country once school is over. Also...

Signed up for US army through MAVNi and getting married to US citizen

You are fine..plan to get married and file for residency first. After three years in residency then you apply for naturalization. Good luck.

What do I need to do next

You don't seem to be eligible for cancellation since you did not have a 10 year presence when NTA was issued! If you do have a 10 year presence and...