Can my boyfriend, father of my child and his mum sponser me for f1 visa?

Any US Citizen or lawful permanent resident could submit an affidavit of support on your behalf for a nonimmigrant student visa.

Can I build a company when I'm in H1-B visa?

On an H-1B visa, you are only permitted to work for your H-1B employer.

Can I marry a Mexican national in Mexico and apply for him to come here after he lost his green card over 20+ years ago?

There is no waiver for drug trafficking and the 3-4 prior deportations make it look very unlikely that this gentleman could be readmitted to the US.

Can the charge of 1st time marijuana possession under 30 grams prevent from returning to US, if there hasn't been a trial yet?

One simple possession conviction for less than 28 grams of marijuana can be waived as a ground of inadmissibility under Section 212(h).

New H1 approved, filed through an consultant. Can I take full time jobs?

You could definitely anticipate an RFE and hassles if you never report to work for the petitioner.

One category means work authorization base don a VAWA self-petition and the other means based on Deferred Action Status.

Can my Fiance ,that now has a pending K1 Visa, still visit me with her tourist VISA?

She could be refused admission as an "intending immigrant."

Till when my employer can file for H1b extension

The extension request should be filed on or before October 10 2014.

Can a US immigrant get US immigrant visa for spouse he married abroad but the couple did not live together?

The USCIS and DOS may suspect that the marriage is fraud is the partners did not live together.

My son married in Paksitan but he and his wife intermingled but did not live together.

A marriage is valid for US immigration purposes if valid in the jurisdiction in which it was entered into and no contrary to US public policy.