As for CYA, you've got two choices. You can treat it like one would a pool and add 30 ppm of pure CYA to the water or you can just use Dichlor as your chlorine source until you build up around 30 ppm CYA, so using Dichlor until you've cumulatively added 33 ppm FC and thereafter switch to bleach (possibly adding one day's worth of Dichlor once a month to keep up the CYA level that usually drops around 5 ppm per month in a hot spa). Either approach is fine. The initial CYA will technically give you a more consistent active chlorine level almost immediately, but that's not a big deal. I assume you are following the
Using Chlorine in a Spa instructions.
The hot tub cover should not leak so a tub should not fill with rain water. A new cover shouldn't have that problem.