1) That's warning and not error. You can ignore it.
2) That's java problem.

What makes you believe NW server is not running? None of these two are related to NW server functionality.

This error is definitely related to the NMC installation. Possibly a problem with the java version. You would need to ensure that the version of jre installed on the machine where NMC is installed, is compatible with the NMC version.

You can cross check if NW is running by looking if a process called nsrd is running.

Sorry I may have missed it, but I'm having problems with a new Networker Fast Start implementation. Everything is installed, but when we try to log into the management console for the first time, it just doesn't do anything. We're running 7.4 SP3, the current Java is 1.6 release 7 on W2K3 R2 SP2. Where can I find the compatibility matrix for NW as it relates to Java?

For separate problem please open separate thread.