[tradedash]

> Would the solving of the problem have a "difficulty" that could be adjusted to ensure that blocks appeared approximately every ten minutes

I am fairly certain you can design your problem to behave in a similar manner or in some manner that increases the complexity based on some criteria

> Is checking that the solution is valid a very fast operation?

That's the NP part in my question. Plenty of scientific problems out there that are fast to verify hard to compute. Ex. Prime Factorization

> Are we sure that there is no "final" answer which would make the calculation unusable at some point?

I would argue, and I might be wrong due to my ignorance on the subject here, that we can never "know" that. That's why P=NP is still an open question