I am a student In CPT part-time (June 1-Aug 15).I have worked >80 hrs in June.Can I work < 80 hrs in July to average it 80hrs.

any time someone manipulates the rules you should not trust them, so go see your school DSO.

Can an employer file I-129 for me while my F-2 is pending?

you have to be in status to change it so if you withdraw the F, then you will have no status as of the filing date.

How many persons can i sponsor?

as many as your income will allow. check the poverty guidelines to see what is the required amount for number of people you are petitioning.

I have A2 visa due to my work. I will begin my studies in the US and ask for F1 visa. Can I keep the A2 visa while I study?

you can have only one status at the time, not both.

Can I travel to mexico for 3 days in july with H-1 B Approval and OPT Extension EAD card which is valid till Nov 2016.

you will be able to if you have a visa to go to Mexico, and if your H-1 is tamped in your passport.

Do I need an immigration lawyer? I want to get a name change on my passport. What will be the follow up process for a F1 visa.

your name change must happen through India or it's embassy, but you can go back to the embassy to have your visa stamped under your new name in new...

New E3 Visa - Change of Employer

you can file a extension of status for your wife if not traveling with you.

yes an H-4 can be a party to a lease contract.

What to answer in Form I-864 in 'country of domicile' question and I was domiciled in Belgium and re-establishing US domicile.

If you lived in the US for at least 90 days then you can be considered domiciled in the US.

I just married with a US citizen but am a unlegal immigrant from haiti.

if you entered the US legally yes you can whether initially or later under the TPS with an advance parole.