Yes, USCIS will process the application. If it takes an extremely long time you can go to federal court to force USCIS to make a decision.

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Yes, it is considered a "parole" which would qualify one for adjustment of status.

If you are a US citizen or lawful permanent resident, file an immigrant visa petition for her.

Get and save many certified copies of the arrest. Then you can get it expunged if you wish.

It does not seem to me that you committed fraud. It appears your employer may have committed fraud. If you do get served with a Notice to Appear...

TN is easier and faster. The others are great ways to immigrate to the U.S., and they are costly and time consuming.

Unless it relates to your good faith marriage, your employment is not relevant to the I-751.

Generally speaking in the U.S. misdemeanor battery is not a crime involving moral turpitude.

Yes. It depends on the what issue is being adjudicated.

If you need more time than you requested, then you must file another application for extension of status.