You must have the OPT or EAD to work. Can you file a STEM extension?

Waiver of the Exchange Visitor Two-Year Home-Country Physical Presence

You both are subject to section 212(e) so you both need a waiver.

Should the educational degree be in the same major as my job on H1B visa?

Yes the degree should match the job but experience also is a factor.

Can I marry my UK partner of 6 years if we cannot satisfy the financial requirements?

My recommendation is you stop explaining all of this on a public blog and at least consult with a Board Certified Immigration attorney.

F1 VISA extension on passport?

The most likely thing that will happen under these facts is your visa will be refused. It is always risky to try and get a visa late in the school...

I don't know what to do.

Yes, you can and should start the immigration process for you.

Can I switch employer during h1b extension filed and expired h1-b visa and I-94?

The best scenario is to file the new H-1 and extension with the new employer prior to Jan 10 when your current H-1 status expires (at least...

I have a kid born in USA , at what old he can give me a green card ?

The child must be 21 to sponsor you, assuming you are eligible for permanent residence.

The judge agrees the voluntary departure for Taiwanese if s/he can use visa-free back to the US again?

She is barred to returning for ten years.

Green card process for parents?

This question has been answered before and the answer has not changed in the past few days.