At least the Leisure Time test strips actually test Calcium Hardness. Nearly all other test strips test Total Hardness which includes magnesium and is pointless to measure. Unfortunately, test strips are generally not very accurate nor precise. The best test kit to get is the Taylor K-2006 (not the K-2005) since it uses drop-based tests and a count-the-drops method for chlorine measurement. The test kit measured Free Chlorine (FC), Combined Chlorine (CC), pH, Total Alkalinity (TA), Calcium Hardness (CH) and Cyanuric Acid (CYA).
Spa 56 is Dichlor. How much you need to add after a soak depends on whether or not your spa has an ozonator. The
owner's manual for your tub does mention ozone. Do you know if your spa has a functioning ozonator? Without an ozonator, every person-hour of soaking in a hot (104ºF) tub would require around 3-1/2 teaspoons of Dichlor to oxidize the bather waste but with an ozonator you might only need half as much. You should just see how much you need to add after a soak so that you still have a residual of at least 1-2 ppm FC for the start of your soak the next day.
If you use the spa every day, they you are chlorinating it every day. There is no need to shock if you are always maintaining chlorine in the spa and at least starting out with some chlorine at the start of your soak.
For every 10 ppm FC added by Dichlor, it also increases CYA by 9 ppm and the CYA significantly lowers the active chlorine level. At first, this is a good thing since it makes the chlorine less harsh on your skin and swimsuits and it will outgas less, but as the CYA builds up eventually the chlorine may not be able to oxidize your bather waste fast enough and the water will look dull/cloudy and there may be an increased risk of getting bacterial growth especially in biofilms. The standard water replacement interval formula adjusted for person-hours of soaking is the following:
WRI (days) = (1/9) x (Spa Size in U.S. Gallons) / (# of Person-Hours Per Day)
If you were to use the Dichlor-then-bleach method, then you should be able to go at least twice as long between water changes. This method prevents the CYA from continuing to build up after you've put in around 30-40 ppm. If you go with this method, then there are other things you need to do such as lower the TA to 50 ppm and add 50 ppm borates (usually by adding boric acid) and you'd need to use Dichlor for a day or two about once a month to keep the CYA constant since it slowly breaks down from chlorine at roughly 5 ppm per month.
I'll let others comment about the frequency of filter cleaning. I'm guessing once a week, but it probably depends on the size of the filter and the amount of spa use.