Yes, the keystore file is json and contains the encrypted private key.
The private key will never change and does not depend on the number of transactions it is involved in. Saving each keystore file and each password is what you need to do for backup. It is also recommended that you test your backuptest your backup.
The name of the file doesn't lead to the private key: writing the name of the file doesn't backup anything. Again, see How do I backup my ether accounts?How do I backup my ether accounts?