Need help on '90 200 instrument cluster lights

[Dave C]

1) the alt bulb does not *look* burnt and contacts
look good.  How can I test the bulb itself?

You need a multimeter (MM) and begin learning how to use it.  It would have
a setting to test continuity.
 If the filament is intact, you have continuity
Broken filament = no continuity.
Touch the MM probes to the bulb contacts with the MM continuity mode
selected.  If you have continuity you will get the audible beeeeeep sound.

I believe it is perfectly harmless to start and drive the car without the
instrument cluster installed.

You say the system is not charging... but how do you know?  What are the
symptoms?
Dave C.