The TMS install guide doesn't state a specific service pack for SQL, but I'd assume you can upgrade it without issue. Suggest you take a backup of the tmsng database beforehand as well as the server, just in case.
Java is only required if you're running TMSPE on the server. If are using TMSPE you need to use the supported version of Java for the version of TMSPE you have, for TMS 13.2.2 that would be TMSPE 1.0 and Java 6 U33. If you run any other version of Java besides what is documented in the deployment guides, it will break TMSPE.