Can I send something on the anniversary of a customer's first order?

Yes. The anniversary note marks a year since a customer's first order with you, and it ships off until you switch it on under Marketing → Loyalty & stamps. There are no birthdays, deliberately, because that would mean collecting a date of birth. If you also want to give something, an earned gift card rule under Marketing → Gift cards can count Years since their first order and hand over a card with its code on WhatsApp. The Loyalty & rewards tab in the docs covers the anniversary.