If my previous company sells its patents am I obliged to assist the acquirer with new patent filings?

I suppose it is possible the employment agreement you had with your former employer had some commitment that extended beyond your tenure. You should know of this or else demand the new company provides evidence of such commitment. It is not, in my experience, the norm.

Assuming there aren't contractual requirements, then you would be fully within your rights to decline to help. What I might suggest, is that you should put forward the option of supporting the new filings at a contracted rate of $XXX per hour. XXX should be a number no less than $100/hr. I personally wouldn't do it for less than $150/hr and if it is a large company significantly more. In any case you need them to respect the value of your time and the only way to do this is to charge an hourly rate.

The $1 is a quaint custom that I used to experience early in my career. When I signed the documents before filing a patent, the company lawyers would give me a crisp new $1 bill as "compensation". I don't think it really matters because as time went on, the $1 bills became less crisp and stopped being provided at all. In any case, you aren't an employee so such customs are silly.

Just to be clear, I am not a lawyer so this isn't legal advice. If you get threatened by the new company, you may need to consult with one.