How can testnet REP be obtained? Is there a testnet or some other automated source to acquire them? Are balances reset periodically or will the testnet REP I remain available to me permanently?
Testnet REP is given out for free when you create an account through the beta site (https://app.augur.net and/or https://augur-dev.firebaseapp.com). Currently this is the only way to acquire testnet REP, although of course you can acquire extra from other users after reporting!
Balances are reset periodically. This is (unfortunately) not done on a regular schedule, and is instead just reset as needed for development purposes. Generally one of the developers will announce that a reset is happening on Slack. Note that when REP is reset for testing, markets and ETH balances are also reset!