Learn French: Le vendeur m'a donné ces brochures, laquelle veux-tu ? - The salesman gave me these brochures, which one do you want?

Laquelle means "which one" and it must agree with the noun it replaces. Here, it refers back to brochures. Since brochure is a feminine noun, and the speaker is asking for a single one, we use the feminine singular form laquelle.

Could I use lesquelles in this sentence?

Yes, if you wanted to ask "which ones do you want?" instead of "which one". Lesquelles is the feminine plural form. You would use it if you expected the person to choose more than one brochure.

Why doesn't the past participle donné agree with the pronoun m'?

Past participles used with avoir only agree with a direct object if it comes before the verb. Here, m' (to me) is an indirect object. The direct object is ces brochures, which comes after the verb, so donné does not change.

What is the difference between using laquelle and quelle?

Quelle is an interrogative adjective, so it must sit right next to a noun, as in quelle brochure veux-tu ? (which brochure do you want?). Laquelle is a pronoun, meaning it replaces the noun entirely so you don't have to repeat the word brochure.