I assume you are referring to the 2 year foreign residency requirement that some J-1 exchange visitors are subject to. It is CIS policy to deny the adjustment of status application if it is filed prior to either:
1. satisfying the requirement by being physically present in your home country for 2 years
2. obtaining a waiver of the requirement (I-612 approval).
Basically you are inadmissible - just like someone who came illegally to the U.S. or has a serious criminal record....
I assume you are referring to the visa stamp in your passport - not the petition which sets the period of your L-1 stay in the U.S. A visa cannot be issued or reissued in the U.S. (Once upon a time it was possible through the State Department in DC).
So your best bet, if you're eligible is to apply for the visa at a nearby American Consulate in Mexico (Tijuana) or Canada (try Ottawa if Toronto and Vancouver are too booked up). Each post has its own rules about 3rd county nationals, so...
The question is confusing since I-751 and VAWA petitions are different critters that only relate to each other in the sense that they involve green cards and domestic relationships. However, it should not make a difference who is the petitioner as long as the marriage was bona fide.
Yes you can - and if you can afford it - you should.
The H-1B petition should filed a.s.a.p.
Given the filing fees involved in the H-1 petition you should see a qualified immigration lawyer immediately. I'm sure you would go see a doctor if your well being for the next 6 years depended on it.
When you pay your filing fees for the I-485 it includes the I-765 fee (like it or not!), so if you include a completed I-765 (a one page form) you'll get a new EAD valid for a full year. You probably wont need it if all goes well with your green card case since you hopefully will have your green card by September. However, if there are delays in the processing of your case, you might be happy you applied for the second EAD which will be valid for another 6 months or so after your current EAD...
In theory, yes.
However, they could also deny the visa for fraud (you lied about being arrested). Although there is a waiver for that as well it is discretionary. The reason you gave as to why you answered "no" would probably not convince the consul that your misstatement was not willful or intentional. Once there is a fraud finding it remains on your record for life.
There are both NON-IMMIGRANT investor provision (treaty investor or E-2 visa) and IMMIGRANT ("green card") provisions. Not all countries have treaties with the U.S. so it depends on your citizenship if you can apply for the temporary treaty investor visa which requires a smaller investment (I usually tell clients at least $100,000 - but legally there is no dollar amount required). The immigrant investor category normally requires a $1 million investment creating 10 new jobs in the U.S. but...