Is there a swimming pool here?

No swimming pool, just two hot jacuzzis and a cold pool not big enuff for swimming

Yes there are pools, but not really "swimming" pools. The pools are just for you to relax and lounge in. There's a warm pool, a warmer pool, and a hot pool. There's also a cold pool, and a steam sauna.

Nude bathing/jacuzzi inside the respective locker rooms

Not really a swimming pool, but they do have the different temperature baths/ jacuzzi pools