"'Help!! have i got spyware on my G4'?", it is quite doubtful that you do.
'In the last few weeks ... Applications will unexpectedly quit especially Word ... asking me to restart ... or asking for a remote debugger and now my mouse pointer has started doing random things ... I haven't added any new hardware. What is going on?'
Unknown information:
Explicit Mac model - 'Sales Order Number' from 'System Profiler's ('/Applications/Utilities/' folder), 'Hardware's 'Hardware Overview' list.
Explicit System / MacOS X version - for example, 9.2.2, 10.1.5, 10.4.3.
Word version.
'... mouse pointer has started doing random things', is not non descriptive. Be descriptive.
What software was installed and / or deleted 'in the last few weeks'?
What attempts, by or for you, were made to resolve the listed problems?
Did you open (run, launch) 'Disk First Aid' / 'Disk Utility' from the (unknown version System / MacOS X) installation disc and attempt to repair the (unknown model) Mac?
If MacOS X is installed, did you open (run, launch) 'Disk Utility' and click on the 'Repair Disk Permissions' button? (this process should be repeated at least once; after clicking the 'Repair Disk' button [a process that should also be repeated, at least once]).