Yes, many stakepools or other parties can use the same oracle. Right now, I think that nut.link is the major oracle that is actually running on mainnet, though it doesn’t report that delegation data that you want. It sounds that there are several large efforts to deploy oracles on Cardano when the Alonzo fork occurs. There is discussion about this in other parts of this forum: Will Ada develop their own oracle pool on chain? - #3 by Kindergarden.
In Option 1 the oracle doesn’t hold any PIGY or ADA, the oracle only provides information to the transaction.
Yes, in Option 2 a javascript or other program could query a service like pooltool.io to see which addresses are delegating to the stake pool and how long they have been delegated. The program could then do the PIGY reward computations and create transactions to send the right amount of PIGY to the correct addresses. I think that some SPOs are already doing stuff like this: searching this forum or google will probably lead you to them, or maybe they’ll chime into this thread and assist.