Answer to Question 1
The surety bond indemnity agreement provides that the purchaser of the bond will pay the surety company back for any losses that it incurs in making good on its guarantee to the obligee.
Answer to Question 2
The three parties in a typical surety contract are the principal or purchaser of the bond, the surety company that issues the bond, and the obligee to whom the surety company guarantees then contractual performance of the principal.