Trichlor tabs dissolve fairly slowly and fairly evenly. They usually don't fall apart. The rate of dissolving will slow down somewhat when they get much smaller since that rate is roughly proportional to the surface area. The pH should be dropping given your fairly low TA of 50 that you last reported. Is the pool covered or uncovered? If you were to add 10 ppm FC to the pool using Trichlor and that chlorine was used/consumed at about the same rate it was being added, then the pH would drop from 7.2 to as low as 6.8 except for carbon dioxide outgassing. So normally you have the pH start out higher when using Trichlor and usually have the TA higher as well. Even if you started with a pH of 7.7, with the low TA the pH after 10 ppm FC would end up at around 7.0 if there were no outgassing.

As for pump run times, you usually figure on one turnover per day but can adjust to keep the water clear. The right amount depends on your circulation. If it's really good, you can sometimes go shorter; if not, then longer; but one turnover per day is pretty typical. Note that an above-ground pool often has terrible bottom circulation since there aren't usually many returns and there isn't a floor drain. Pointing a return diagonally downwards sometimes helps with circulation.