It is one of the many, rarely shown rooms of the Tardis. While only shown a few times since the 60's, usually indicated by a splash noise or a wet/damp looking character, it is assumed that it is a permanent fixture
Yes the TARDIS does have bedrooms, it changes each time the Doctor regenerates, currently it also has a swimming pool and a library along with the bedrooms
The Doctor has a sonic screwdriver, TARDIS, companions, age, intelligence, a swimming pool, a library, a wardrobe, and cool clothes. (To name a few).
Yes and the swimming pool will make it fade much faster.
um, i don't really know what you mean by similar to a library, but in the episode "the 11th hour" with Matt smith, they mentioned there being a library IN the tardis, right next to the swimming pool. The tardis library came up again in "amys choice" when the doctor says hell just "pop down to the library for a swim"
They thought hey let's make up a band and call it. Come jump in my swimming pool :))
Yes
'Swimming Pool', sometimes shortened to 'Pool'.
Probabily the ground surrounding your pool if its in-ground. In an above-ground pool they most likely fly into the pool or crawl into it from the sides.
What are swimming pool "Coopers"
it depends on which swimming pool
Can't be answered, as pools come in different lengths.
No, they can't swim.