Learn French: Le buffet près duquel tu es resté est vide. - The buffet near which you stayed is empty.

This sentence uses the preposition phrase près de (near). We need to say "near of which" to refer back to the masculine singular noun le buffet. When the preposition de combines with lequel, they contract to form duquel.

Since dont can mean "of which", could I just say près dont?

No, you cannot use dont directly after another preposition. The word dont replaces de plus a noun, but only when de is standing alone. Because de is part of a compound preposition here (près de), you must use the duquel forms.

Why does this sentence use es instead of as in the past tense (tu es resté)?

The verb rester (to stay) is one of the special verbs that always take être (instead of avoir) as their helping verb in the passé composé. These are the verbs you might have learned using the "Dr. Mrs. Vandertramp" memory trick.

Would the spelling of resté change if I were speaking to a woman?

Yes! Because the helping verb is être, the past participle must agree with the subject (tu). If you are speaking to a female, you would add an e to the end and write tu es restée.