If a subeona was taped to a door and while removing the subeona from the door paint came off the door.
1. Can the firm who "nailed/taped" the subeona to the door be sued for damages?
2. Can the law firm who hired the company to serve the subeona be sued for damages?

In theory, yes, your property was damaged. In practice, how much was the damage?

I've taped more than a few legal documents to doors and never, ever have I damaged the paint.

But, yes, if you have the time, money and energy to follow through, go for it.