Can a convicted us citizen marry a non US citizen without affecting their ability to apply for green card & sponsorship

Yes. Please see

Can I register a company in another country and work in US for it on H4 visa?

An H-4 visa does not permit one to work in the U.S. Please see

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Green Card process?

There is no waiting period before an employer can sponsor you for a green card. Please see the following video:

If I won DV : can I enter USA "temporarily" on B1B2 visa ?

Since you have expressed an intent to immigrate to the U.S., it is doubtful whether you will be allowed to visit the U.S. on a temporary tourist...

Will I be out of status if last day of employment with employer on H1B is Oct 25 and H1B transfer application mailed Oct 27?

Yes, you should apply for a change of H-1B employers BEFORE you stop working for your first employer. Please see

Immigration appeals

Once the Judge issues a decision and you appeal, the BIA issues a briefing schedule. You get a certain amount of time to write a brief and ICE...

I'm an E2 Dependent with an employment authorization. Can I work as a real estate agent?

You can work in any job you wish. Consult a CPA regarding tax forms.

Illegal Immigration& sick child

If your wife does not want to apply for a green card in CDJ, her alternative is to apply for cancellation of removal before an Immigration...

Lie in visa application

Of course, lying on an immigration form is fraud. This can have terrible consequences.

L2 to H1B

Yes, you will need a change of status. Please see