Learn French: C'est la salle de bain pour laquelle j'ai acheté un miroir. - It is the bathroom for which I bought a mirror.

The relative pronoun has to match the gender and number of the noun it replaces. Here, it refers back to la salle de bain, which is feminine singular. Therefore, you must use the feminine singular form, laquelle.

Could I put pour at the end of the sentence, like we do in English ("the bathroom I bought a mirror for")?

No, French never leaves a preposition dangling at the end of a clause. While in English we can say "the bathroom I bought a mirror for," in French you must literally say "the bathroom for which I bought a mirror" (la salle de bain pour laquelle). The preposition must always sit right in front of the relative pronoun.

Why does the sentence start with C'est instead of Elle est, since a bathroom is feminine?

You must use c'est because it is followed by an article (la) and a noun. You only use il est or elle est when describing a specific thing using just an adjective, for example: Elle est propre (It is clean).

Is it also correct to write salle de bains with an s at the end?

Yes, both spellings are totally correct and common! salle de bains (room of baths) is the traditional spelling, while salle de bain (room of bathing) is also officially accepted and used everywhere.