It is fairly easy to kill the yeast in my experience. Using too hot water to make the initial mix or activate it. Needs to be luke warm at best (I believe 105 degrees is max, personally I just barely get it warm.) Also I made the mistake once of taking the yeast straight from the fridge and making it up. The temp change was too sudden. Now I just store it in a cabinet.
Not sure what you mean by blowing back through the system to check for leaks. Soapy water is the way to go. Apply it to all the connections, if you see bubbles, there's a leak. However, if you just have the open line going into the tank, there may never be enough pressure to show a leak - but there should still be bubbles coming out from the line.
I would connect the diffuser you have, or use a 1" piece of chopstick, or a piece of regular cotton ball tightly packed in the line. Then wait 8-12 hours to allow for pressure to build, and check for leaks with soapy water.
For a 10 gallon, I'd just go with one 2L bottle + a smaller gas separator/bubble counter bottle. Keep an eye on how many bubbles per second it produces, and change it out as soon as you see it slow down. Probably 7-10 days, possibly 2 weeks.
Or you can get a paintball set-up for probably around $150
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