Generally, an employer can ask you any question they want as long as they are not delving into "protected" categories or activities. These...

Job offer

I assume your real question is whether you will lose unemployment benefits if you turn down that job offer. The key to answering that question is...

Payroll mistakes

Yes, your employer is allowed to recoup monies paid you if they truly made a payroll mistake and overpaid you. However, there are several cases...

Employment / Labor issue

From what you write, I think you certainly have a "last paycheck" claim for unpaid wages. You should be able to find an employment attorney...

Wrongfull terminations

At the very least, your old employer owes you your last pay check. Nor can the employer hold your paycheck "ransom" while they ask you sign...