How many days can I stay in US

This is a specific legal question to your specific fact scenario that cannot be answered here. You need to seek consultation from the immigration...

The questions you are asking should have been asked in your consultation. These are specific questions to your specific scenario that cannot be...

Entry in the US on L2 visa expiring in 7 months

There is no issue here. If you have a valid visa stamp, then you should be fine to reenter the US.

My mom got US citizenship in 1994 through sponsorship but did not come. Would that sponsorship be valid today

Did your mom qualify for citizenship or did she get sponsored for a green card? If she qualified for citizenship in 1994, without having any other...

Green card expires

She can apply for to renew her green card right now, if she desires by filing an I-90. There's no penalty for it being late.

Continuos residency requirement

You are going to have to disclose to the officer at the time of your interview about this specific travel outside the country. The officer will...

Can I travel? Can I have another stamp on my passport? If I re-file a new I-751 for hardship?

You answered your own question in the last line about the denial notice that you received. You cannot file a new I-751 when the prior one has been...

Came into the US with a 6 month tourist visa in April of 2013 and has stayed beyond the limit of time, how can we extend?

Once you are out of status, you cannot change your status or extend your status. A person in this situation is unlawfully present in the US. As...

I-730 for spouse

If you have not received anything from USCIS, you need to contact USCIS. You should have received a receipt notice at time of filing the I-730. ...

Can I file h1b to h4b without leaving US?

You wish to become a dependent of an H1B? As long as your spouse possesses an H1B, yes you could obtain a change of status in the US.