"This is my bathroom."
Translation:Das ist meine Toilette.
I don't know about the first question, but it isn't diese, because it is not followed by a noun. If dies was used as an article here, it would have been diese, but it is not. Meine is used in stead of die here.
Not sure if that clears is up, but I'll provide an example:
It is this bathroom=Es ist diese Toilette
This is the bathroom=Dies ist die Toilette
A toilet and a bathroom are not the same thing in the UK! If anyone used my bath (located in my bathroom) as a toilet I would not be happy!
it would have to be mein Bad - toilet is feminine, bath is neuter