How can I run bitcoind on test and production networks, at the same time, on the same computer? Bitcoin and Bitcoind will send an error if it is launched multiple times.  I'm assuming this is because they share the same database and wallet.

Is it possible to run two instances of Bitcoin QT / bitcoind with one listening on Production and the other on Test? (on the same computer)

Is this advisable or not advisable?
You can run a mainnet and testnet bitcoind next to eachother without problems. They do not share the same database (one will use the testnet3/ subdirectory).

What will conflict is the RPC port, as they will both try to bind to port 8332 for receiving RPC connections. Use -rpcport=N on one of them to use a different port.