Hi and welcome to the Pool Forum!

Your alk is ok. Your pH is ok at 7.2 but if it were my pool, I'd bump it up just a little to get it around 7.4-7.6.

Those tabs in the floater are trichlor, not dichlor. Whether or nor you should be using them depends on the CYA level. What kind of kit is the HTH kit -- test strips or a drops test? Does it have a CYA test that uses the disappearing black dot test? Tell us what happened when you did that test. Does your pool store use the disappearing black dot test?

Also, tell us exactly what kind of expensive chemicals you have on hand. We need to know ingredients and not just 'shock.' Some of those pool chemicals have a lot of stuff in them that can mess up your pool. For example, sometimes products have copper in them. You do NOT want copper in your pool. Contrary to popular belief, it is not chlorine that turns hair and pools green, it is the copper.