Are the immigration authorities treat H1B visa differently if this if for part time job

A part-time job should not be a problem if the company can demonstrate a need for your services.

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Can I stay illegally for 6 - 7 months after my F1 status expires ?

You should not stay unlawfully in the US.

Can I use existing quota ( FY 2013 ) for a fresh H1B Application ?

The petition is subject to the cap and you must wait until October 1, 2013 before you can start working in H-1B status.

Do I need to apply for re-entry form?

You better apply for a re-entry permit before you leave.

Can L2 stay beyond the L1 stay until the validation of L visa ?

Your spouse can enter the US at any place with a valid visa but can only stay for as long as you maintain your L-1 status. If you leave in April...

Green card expired three years ago, i live in Mexico but i want to travel to the US can i renew my card?

I agree with my colleagues. You most likely abandoned your resident status absent significant US ties and compelling reasons that prevented you...

I am on H1 - b visa , got a new offer of employment , can I remain in the US though the new company rescinded the offer ?

You will not be subject to the cap. It is up to USCIS to extend your status through a new H-1B petition although you are already out of status if...

If a petition to adjust status is withdrawn, is affidavit of support automatically withdrawn also?

The I-864 is not relevant anymore if the visa petition (I-130) or adjustment application (I-485) is withdrawn.

USCIS Changed my address when I didn't request to ?

Just call the 1-800 and ask.

File I30 now and upgrade later or file later

If your spouse if already in the US processing will be faster if you wait until you became a US citizen and file all applications concurrently....