1. The agent is correct.
2. It doesn't matter. Separate PNR for the infant won't really affect anything, including IRROPS rebooking as UA is hardly going to route an adult and a 2YOA on separate routes.
3. For the international ticket, UA will simply refund it and when you do travel, you will purchase a new ticket. The infant, of course, will go from 10% to the seat fare.