Can a cousin file for me to get my green card.

No

H1 Extension and PERM related

short answer is you can do it meaning you can file an extension while your labor certification is pending six months ahead of your expiration date....

Can I rejoin old company through an L1?

You should discuss this with the attorney for the employer. If the company has an L-1 Blanket it must have many intracompany transferees. So the...

My wife's ex-husband put stalking case on me and was dismissed, now can I apply of naturalization?

You should be fine. HOWEVER, You should speak with an experienced immigration attorney to assist you with the process to make sure you are...

Some do.

L1 to H1 COS

Where are the attorneys of these two employers? You need to speak with them.

I am a British Citizen on E2 visa, can I transfer my E2 to a international company qualified for E2 but NOT British? i.e German?

No. But there may be other possible options to transfer your temporary work visa. You should speak with an experienced business immigration attorney.

Will the time period of my first visit to usa counted for30/60 day rule applicable for marriage on tourist B1visa? Thanks

You should contact in experienced immigration attorney asap.

Can I start working under my F1 visa status?

Not under the facts you stated.

1. Can I go for STEM Extension simultaneously with GC sponsorship? 2. Can I have F visa for my studies along with sponsorship?

You should speak with an attorney.