I agree that framing it is the right way to do it. You might not need a permit if you're not closing up the framing and aren't planning to run new electric lines. Check with your local permit office. They will be happy to tell you what is and is not required. They are not police, so they aren't going to do any investigations later on.

Framing for something like that isn't too tough if you're a semi-decent woodworker. Youtube should have enough info. Just do the framing correctly so that if you want to do proper finishes later you'll already have it.

For the floor, it is probably better to leave it unsealed. Properly sealing a concrete floor is not trivial and doing it wrong can cause bigger problems. If you don't want to work directly on concrete, consider some interlocking foam/rubber squares.