How many holes for the faucet are there in the sink?

Vanity top is pre-drilled for two 4.02"/102mm widespread faucets (faucet not included).

Can you recommend bathroom a mirror that fit this vanity?

Yes, please have a look at this link: https://www.homary.com/item/modern-oval-24-x-32-rgb-led-frameless-bathroom-wall-mirror-antifog-41202.html

Are the pop-up drains included?

No, I recommend you this pop-up drain : https://www.homary.com/item/gold-finished-popup-drain-assembly-without-overflow-for-bathroom-vessel-vanity-sink-10855.html

Can you recommend faucets that fit the sink?

Yes, please have a look at this link: https://www.homary.com/item/mooni-modern-waterfall-widespread-2handle-bathroom-sink-faucet-in-gold-solid-brass-10992.html