Learn Polish: Powinieneś sprawdzić przestronną łazienkę, w której nie ma wody. - You should check the spacious bathroom in which there is no water.

Której refers back to the feminine noun łazienka (bathroom). Because it follows the preposition w (in), it must be in the Locative case. The feminine Locative form of the relative pronoun który is której. If it referred to a masculine or neuter noun, you would use w którym.

Why do the words przestronną łazienkę end in -ą and -ę?

They are in the Accusative case because they are the direct object of the verb sprawdzić (to check). The dictionary form is przestronna łazienka. In the Accusative case, feminine adjectives change to end in -ą and feminine nouns change to end in -ę.

Does the word powinieneś mean the person being spoken to is a man or a woman?

A man. Powinieneś is the masculine form of 'you should'. If you were telling a woman that she should check the bathroom, you would use the feminine form, powinnaś.

Why is it wody and not woda at the end of the sentence?

Wody is the Genitive case of woda (water). In Polish, the phrase nie ma (meaning 'there is no' or 'there is not') always requires the noun that follows it to be in the Genitive case.