How can a foreign company sponsor an H1B visa in the US?

The answer to your question is too involved for this forum other than say speak with the company attorney or go to www.uscis.gov.

Based on your love story facts a K1 visa is available. Given you say you have no idea what to do, meet with an immigration attorney.

My student visa expires in Dec-2017. while change the study I am not getting admission for 6 months.. Can I stay in USA ?

You are not allowed to be in the US without status.

Can I apply for a wavier after having an intention of violating the terms of my tourist visa?

Regulations make it very difficult for you in either circumstance.

Can i apply for motion to reconsider if my visa was expired and the decision on my asylum application was refferd to im. Judge?

Regulations permit you to take up this matter before the judge. Suggest you hire an immigration Attorney.

My mother in law has a green card but has been out of the country for more than 4yrs due to my father in law's ill health

Green card has been abandoned, so she will need to have someone petition for her, probably while she is outside the country to avoid saying one...

Naturalization Part 11- Question 34-35.

We cannot give advice through this forum but note you voluntarily departed.

Hi, what is the general fee for an hour consultation with a immigration attorney in LA?

As different as there are stars in the sky. Calling around is best bet.

Can I used my dad W-2 and my dad Tax Transcript to sponsor my mother?

It is permissible for your dad to be a co-sponsor as long as he meets the financial qualifications.

B1 visa validity ??

A B1 visa is good for up to one year.