If I want to work with a particular address, I need to know all the transaction indices/hashes that have inputs or outputs to/from that address. How can I find out those values assuming that I have the Bitcoin core installed and synced. Is there a command I can give that will return that information for a given address?
Bitcoin Core has no option to maintain an index of addresses, thus you cannot search by address or search for things related to an address.
The command you're looking for is the listunspent command, which lists the UTXOs in your wallet and gives out the txid and output index for each one.