Learn Russian: Это ванная, в которой нужен новый ремонт. - This is the bathroom in which a new renovation is needed.

Который (which) has to match the gender and number of the noun it refers back to. Here, it refers to ванная (bathroom), which is feminine. The case is Prepositional because it follows the preposition в (in). So, it becomes the feminine prepositional form которой.

Why does ванная have an adjective ending (-ая) if it is a noun?

Ванная originally comes from the phrase ванная комната (bath room). Over time, people dropped the word for room, and the adjective ванная became a noun on its own. Because of this, it still uses feminine adjective endings when it changes cases.

Why do we use the masculine нужен here if we are talking about a feminine ванная?

Нужен (is needed) must agree with the subject of its own part of the sentence. The subject inside the relative clause is ремонт (renovation/repair), which is a masculine noun. Therefore, we use the masculine нужен, not the feminine нужна.

How exactly does нужен новый ремонт work here instead of using a verb for 'to need'?

Russian does not have a direct, commonly used verb for 'to need'. Instead, it uses the short adjective нужен (necessary or needed). The literal translation of this clause is 'in which a new renovation (subject) is needed (adjective)'.