You use 不 for every verb except for 有, where you have to use 没 for the negation. It is explained in the Tips and notes section of the Family 1 lession.

不 is used with 是 and 没 is used with 有.

I found that only 没 negates 有.

The other two are correct, but I've never heard of 浴室 used in the context of a restaurant's restroom.

Yes, think of it as the staff speaking on behalf of the restaurant.

If you would use 一个, you would be saying "sorry, we do not have one bathroom", which would be strange in either language. Chinese doesn't have articles like a/the

No. Actually it shouldn't be added.

Yes.

有 is the only special case where you negate it with 没 instead of 不. It is explained in the Tips and notes section of the Family 1 lession.

没有 is the default negation of 有. This is ONLY the case for 有，other uses of 没 are essentially negation in the past.