Is this legal? Lunch deducted from hours, but still working.

I agree, I would urge you to contact the department of labor.

Shortage in pay over 2 weeks

She should contact the department or labor if they do not pay her right away.

What do I do? Labor law violation?

Complain to the State Department of Labor or speak with a local employment attorney right away.

Do employees have to work in extreme heat conditions?

Consider contacting OSHA if you do not have a union to turn to.

What type of lawyer do I need? What would you suggest I do?

They're trying to leverage your crime to force you to pay extra. Speak to a local employment attorney and negotiate down.

If the post does not have your name in it, I am not sure how it could be connected to you in a background check.

Do I owe my former company money?

If they mistakenly overpaid you, then yes it is money you will have to pay back. If you have something in writing stating otherwise, then meet with...

Do i have to repay a relocation fee if i do not stay at the job long enough?

We don't know the terms of the contract you signed, but if they fit the situation and call for repayment then yes you may need to repay them.

Can I be fired for refusing to sign a paper agreeing to turn my my cell phone off ?

Yes, you can be terminated for that. Why not simply provide your grandmother the office line for emergencies?

What kinds of problems will arise if a foreign worker receives payment into his US-bank account from a US company?

In terms of employment laws, none that I am aware of. But I could not advise you as to the various immigration, money laundering or other...