where I can rent a cabin/cottage with a fireplace, possibly next to a beautiful lake or forest or mountain?
If you want mountains, Zakopane or nearby would be the place to go. There is a very beautiful lake about 15 kms away, Morskie Oko. Whether there are cabins near the lake I don't know, but you could try e.g booking or other sites.
Masury lake area is also meant to be very scenic, but no mountains I'm afraid!