While this post has turned into a name-calling forum, I wanted to mention just a couple of things that I don't see addressed.
If you've had this pool guy for 6 years and he's been doing the same thing for this entire time, you definitely have a problem. Putting trichlor in the skimmer, and worse, crumbling up a tablet into the pool, is wrong and amatuerish. There is a reason they have tablet feeders and I recommend, if you intend to keep using trichlor, you get one. Don't use a floater, the renters can remove it (and will) and they can drift and find a home in a shallow swin-out or over the steps and cause staining.
The reason they shouldn't be used in the skimmer is they are acidic. 6 years of putting tabs in the skimmer has been eating the inside of your pump basket, impeller, your heating element and, if you don't have PVC plumbing, it's been stripping your plumbing which results in many other problems.
It can also effect your sand. I disagree with the guy who says changing the sand is a myth. Fast moving water (even slow moving water) flowing over/through sand/stone will smooth the surface of the sand/stone. The filterability of the sand relies on the rough, porous suface of the sand. Remeber, the Grand Canyon was carved through the earth by water flowing over land/rock over a period of years.
Also, the higher acidity of the high pressure water, due to the tabs in the feeder, can cause the break-down to occur even faster.
Your low pressure in the filter could be related to your impeller due to it being slammed with acidic water for 6 years. It's threads could be worn and it may not be spinning as it should or it's channels could be worn down and your flow is insufficient. This would also be a cause algea growth. Bad flow and poor filtration mixed with the higher levels of Cyanuric Acid and hot temperatures is a perfect storm for algea blooms.
Much of the other advise you have already received addresses the issues well. I just wanted to clarify on those issues which had not been addressed.