Welcome to the community, ProContractor.
1) Should I tell the hiring manager about my last contract situation up front? And then let him decide if that matters or not.
2) The hiring manager may not know what happened to my last contract and may think it ended naturally. If I don't mention it and he finds out down the road (say after one month I am on the job), will there be any problems for me?
3) I don't know what record the HR may have kept on me. It could be nothing because the PM was a known trouble-maker with other people and was laid off by the company shortly after I was let go.
4) If I go to work in the new group, will I feel awkward? I will not work on any projects with people in the original group, but will see them in the building.
My own opinion:
Why is it your problem to do this client's due diligence?
Every business can surely pool its collective internal knowledge. This is the easiest possible type of dirt to collect on someone. And two years is a
long time.
My own tendency would be to pursue this as far as they want to take it. Money is money and business is business.
I even have an alternate explanation for this bizarre turn of events: manager #2 and his informants already know the story and they also have inside knowledge that your firing was a stupid move by manager #1. They believe that you are useful and they like you.
And would you expect anyone on the hiring end to say
anything even if they knew? If their opinion of you is positive, they would probably rather be discreet about it and proceed without any fanfare.
Either is equally possible given what you know at present.
I would "bull on" through your self consciousness of this new contact and see what happens. A lot of times it is an opportunity for personal growth to stick your neck out. And I see this as riskless.
Good luck, either way you go.