Just some observations.
1. The VTS is not working because water entered through where the boot is missing. Since you said you want it working a temporary fix would be to remove the VTS motor, inside you'll find a large plastic, move the block about halfway and reinstall the VTS motor.
2. Stay with the same oil the previous owner used.
3. Yes change the grey tempo fuel lines ASAP.
4. PM minnetonka4me and get some good used gauges.
5. The check valve/vent on the top of the oil tank is correct, a hose does NOT connect here.
6. From outward appearance it looks like the carbs. were recently rebuild, the return lines from the carbs. to the "Y" connector look new, it would still be a good idea after you replace the fuel lines to take a look inside the carbs. and also clean the carb. filters.
7. The small oil injector lines have been replaced with tygon lines, this is good.
Overall the ski looks real good and with the exception of the fuel lines, and the VTS the previous owner took good care of the ski.
Lou