What is the TX key?
I know it is related to $r$ from the whitepaper, but I'm not sure which number it is. (I'm thinking it is either r, rA, or H(rA)).
The private tx key is named r in the CryptoNote whitepaper. Note that r is randomly chosen. In addition, the private tx key can be used as prove of payment on a case by case basis. That is, in case of a dispute, you can prove that you paid the receiver by publishing the private tx key (which you can obtain from the wallet), the transaction ID, and the receiver's address. An auditor can subsequently verify that you paid the receiver.
The public tx key, which is embedded into tx_extra, is R, where R = rG. This graph of luigi1111, which is originally from the CryptoNote whitepaper, might be helpful too: