It’s helpful to have a local attorney review your situation. However as mentioned some professionals including certain H1b employees are exempt...

A student can have more than one residence

I don’t see how that factors into a worker’s comp claim. Consult with a local attorney for evaluation of your case.

Consult with an attorney to draft a demand letter. Failing which the attorney can file a lawsuit. A class can be formed.

It is possible to be paid more than what’s stated in the filing papers

It is advisable to work for the petitioner employer for at least 6 months to avoid the presumption of fraud.

Stay out of the country for that amount of time raises a presumption of abandonment

1. There is no need to list this job 2. I do not see an impact to the N-400 application

Your disability must fit the definition as provided by the ADA. Consult with an attorney as soon as you can.

Consult with an attorney to assess your rights and take next steps on your behalf