Question on Cooling off period

Typically an employer hires an immigration attorney to assist with an H1B petition at no cost to the employee. You should consult that attorney as...

Can any company file a H1B Visa?

Congratulations in your job offer. Any employer with a job vacancy can apply for H1B visa. However, they should consult an immigration attorney.

Your case is too complicated for a quick response in a public forum. You need a consultation with an experienced immigration attorney.

Will my F-1 visa application suffer because of my husband's current H-1B status?

No. An H1B visa does not confer immigrant status in the US. You may still qualify for F1. in addition, you might qualify for H4.

Affidavit of support when applying for Green Card.

They may still qualify based on their current income and how likely they are to maintain their income above the poverty line.

Граждане зарубежных стран могут подать заявление на получение визы L-1, если они постоянно работал в компании у себя на родине

You should consult an immigration as soon as possible.

H4 candidate is in USA while H1 candidate is in home country for short visit and visa stamping.

If she is still working for the employer, she is not out of status, therefore you are not out of status either.

Am I allowed to open an offshore company FROM the US as an International Student and open an American business account for it?

You are not allowed to work in the US while on a F1 visa. It is illegal.

Spousal sponsorship Green card

If you received a J-1 waiver, you do not have to go home for 2 years in order to adjust status.

Possible concurrent file for F1 and H1B, what could happen to my H1B petition?

It should not. Each petition is handled separately and must be supported by evidence.