Promo Code of $20.00 off service: if I send this to multiple people, is there a limit of how many people can use the code to get the discount?

No. There is no limit, as long as they are "new to rover customers". If they book with you, the new customer gets a $20.00 discount. If they use your code but book with someone else, "YOU" get $10 (if I remember correctly or if rover hasn't changed their rules on the promo code.)