Massachusetts - Question Re Employment Termination And Unemployment

Massachusetts. I just got fired. I plan to contact some lawyers tomorrow morning, but wanted to ask some questions here regarding next steps:

I have been extended a written offer to continue my full pay for 3 months and insurance for 6 months. In exchange, I am not to make any direct or indirect statement or that may paint my employers or any involved party in a bad light, or take any action against said parties. The existence of this offer can only be disclosed to other parties for my legal counsel and as allowed by law.

1 – Employer has let me know they would not contest an unemployment filing. If my unemployment claim is accepted, would this negate the pay from the above offer extended to me?

2 – I have received two written checks: one as pay for the day, and one for accrued time off. They have a bunch of numbers and calculations attached to each one. Would my cashing of either of these checks constitute an acceptance that the amount provided is correct?

Thanks in advance for any information you may have to offer on my case.