Translation:Why is there no mirror in the bathroom?
Mi portas pluvombrelon, ĉar pluvas. = I am carrying an umbrella because it is raining.
Mi portas pluvombrelon, tial pluvas. = I am carrying an umbrella; that's why it is raining. (= ... and because of that, it is raining)
Ambaŭ donas kialon, sed en la unua frazo, la pluvado estas la kialo por la portado de pluvombrelo, sed en la dua, la portado estas kialo por la pluvado.
That would imply that there is a mirror somewhere. Whereas the original sentence doesn't imply it. There could be no mirror in the house at all and someone may still ask the original question whereas yours would be grammatically incorrect due to the presence of the mirror, or rather the lack thereof.
Word order: one starts "why there is..." and the other starts "why is there...".
As a normal question in English, it has to be "Why is there ...?".
The other word order would be used in an indirect question, such as in "I don't know why there is ...."
You can't use one word order in the other situation.
I'm guessing from your name that you're Dutch? Isn't it similar there? "Waarom is er een spiegel in de badkamer?" maar "Ik weet niet, waarom er geen spiegel in de badkamer is" with different word order.
A necesejo is a room with a toilet. It's a room for "performing the necessities" - defecating and urinating.
A banĉambro is a room with a bathtub, a shower, or at least a sink. It's a room for washing.
Some rooms have both, but not all, so if you want to empty your bladder and ask for the banĉambro, you may end up in a room with a bathtub and a sink but no toilet; and conversely, behind a door marked necesejo you may not find a shower.