How many REP (Reputation) tokens exist? What is the rate of inflation (if any) in REP supply?
Since REP is not mined, what security mechanisms protect its supply and ownership records from being altered?
There are 11 million REP tokens today and there will always be only 11 million REP. REP can be bought or sold but the supply of 11 million REP remains the same.
If a reporter reports incorrectly, they lose any REP they staked on the incorrect outcome, but that REP does not disappear, instead it is reallocated to reporters that reported correctly, so the total supply of REP remains the same.
As an ERC20 token, REP ownership is tied to an Ethereum address. Ethereum is an immutable ledger protected by miners. REP transactions can only be conducted (and verified by miners) if the owner of the ETH account where the REP (ERC20 token) is associated signs the transaction or in cases where the REP owners fails to perform his/her duties and suffers a penalty.
As pointed out by Micah Zoltu in the comments below REP can become inaccessible if a user registers to report and then fails to show up to do so. If a fork occurs and not all REP migrates to the same branch, then each branch would have less than 11M total supply (though all branches combined will still have 11M total supply). As with any ERC20 token if the private key controlling the Ethereum account where the REP resides is lost, it will also become inaccessible to its owner although the total 11M REP supply once again would remain the same.
In the Augur Whitepaper it states that after a fork, all users who migrated their REP to the child universe get 5% additional REP tokens which are minted out of thin air.