Wow!

The obvious assumption I'm going to make is that your pump is about 2 1/2 times more powerful than you need--no wonder you've burned out 3 pumps quickly--3 pumps in 5 years is insane! I have a much larger pool, and use a 1 hp pump, and it's into its 8th season with no problems. Whoever sold you that pump was totally irresponsible--that pump would probably suit a pool with 3x the volume of yours! Had you replaced BOTH the filter and pump with properly matched units, you would not need to replace it again for many, many years, saving yourselves a fortune in the long run. In fact, I wouldn't be surprised if your filter is badly damaged--I'd be surprised if it's not!

You don't say what kind of filter you have, nor what size it is, but I'm guessing it's a sand filter since you backwash. For a pool your size a pump as small as 3/4 hp may be perfectly adequate--and save you a fortune on electric bills.

Do you have a pressure valve and what is its normal reading? That will help us tell what's going on.

The T-Valve is just the same as ball valve only you pull it up to open (I think) and down to shut (I think). I have a ball valve instead on my skimmer, but it's the same. The T-Valve is NOT there for backwashing. NOT!!! I ONLY close the ball valve to backwash if my water is too low and it starts sucking air. I'm assuming you have a low drain as well. If not, you NEVER close that T-Valve--you'll destroy your pump.

If, when you backwash and the skimmer is sucking air AND you have a low drain, you close the T-Valve. Otherwise, leave it open.

The T-Valve is to make it easier to clean out the pump's skimmer basket. You close the T-Valve (and the valve from the low drain if you have one), and set the Multi-valve to CLOSED to open and clean out that basket so you don't have a gusher. If you do NOT have some sort of shut off you need to plug these openings.

(My dad had a kind of rubber cork he stuck in that had a butterfly handscrew to tighten and expand it to seal it. Pool stores still sell these and Home Depot sells a version of it for plumbers).

Again, though, I'm sure your main problem is an oversized pump. Horsepower in pumps is NOT like horsepower in cars--more is NOT better! It destroys filters and wastes electricity.

Please fill us in on more information if you can.

And please understand that I'm trying to help. We all have been ignorant about this stuff at one time or another and we all have been taken advantage of, too. The pool industry is cram-packed with people who sell folks stuff they don't need and even stuff that DAMAGES their equipment.