If I book a round-trip infant ticket for a child who is 18 months old on the moment of the trip but becomes 25 months old on the return leg, how fare is calculated? And what about award flights?
The kid needs a valid ticket of her/his own for the return leg. You can either book a full round trip ticket for the entire flight or buy a separate one way for the return only.
Same rule applies regardless whether it's an award ticket or a cash ticket. Main difference: a one way award ticket tends to be half the miles/point of a round trip ticket whereas a one way cash ticket is typically more expensive than half the round trip fare and in some cases even more expensive than the round trip.
The safest approach is to get a round trip ticket for the kid. This way he/she can be on the same booking/reservation as you and if anything needs to be cancelled or changed, it all stays together. You also get a dedicated seat for the outbound leg, which makes travel more comfortable.
EDIT: Some online systems won't give you a separate ticket for a kid under 2: you may have to call the airline to get the round trip ticket booked or just make the kid older on the online booking system.