We are sorry to hear of your issues with your pool maintenance folks. Let’s see if we can help.
It looks like you have a Pentair SAL (Spectrum Aqualight) which were pretty spiffy lights when they came out - there were not a lot of options available back then for color-changing pool lights like these.
To answer your questions:
The pool lights may be the same as the spa lights. If they are the same physical size they are probably the same.
Fixing or repairing the light is probably out of the question. Most of the parts are obsolete and will be difficult/impossible to find.
Replacing them entirely is your best option. You will need to know the size of the niche that the lights are installed in for replacements, but the Pentair Amerlite or the J&J XG-series (available from a brick-and-mortar Hayward dealer) lights should replace them. There are others as well, but, whatever you get, be sure to get replacements that are the correct voltage and with a long-enough power cord.
Check out our guide on How To Replace a Pool Light Fixture for some helpful tips.