If those tabs are about a half pound each and pure trichlor then that only accounts for about 33ppm of CYA so I'd say that 60ppm number was bad.

As you determined, you'll need to switch to an unstabilized form of chlorine. Bleach or Liquid Chlorine (high strength bleach from pool store) is most popular around here.

1)Test for FC, CC, and pH daily, TA weekly (less if you find it doesn't change), CYA a few days after those pucks are all dissolved and then maybe monthly, CH a couple times a season - in your vinyl lined pool, CH is not critical, you just don't want it to get too high as that can cause cloudiness.

2)You might as well let them dissolve, they'll only add a little more to alot of CYA.

3)CYA will drop very slowly as your replace water lost to splash-out and backwash.

4)No, I think your test in May was bad and you've building CYA for years.

5)Copper.

Perhaps Ben will advise you regarding running a pool with CYA at 270ppm.