Battery drainage

what does the alternator put out?

Your diodes in the rectifier could be bad, that will drain it when your TB is in the off position. Will show up good and pass any tests done by autoparts stores. With a volt meter put your meter on Volts AC, yes AC. If you see anything more than say .145 volts, that could be your problem. OR with the alternator out using the diode tester on meter, negative lead to the positive post on alternator, and positive meter lead to metal shell, should be around .505 Battery should be charging at around 14.5V DC with engine running, and around 12+ off.

Would the relays cause drainage as well?

If your drain is happening when your engine is off...You really should check for parasitic draw or drain. You'll need a meter, to narrow down where the drain is happening. Could be a # of places.

On a side note, I just had a brand new alternator out of box fail. Diodes were pumping too many AC volts into the system. Called Ripple

Ok now I have another problem my trailblazer did not want to turn off, it kept returning on and now the starter burned up. I had to remove a fuse to make it cut off

Oh boy, my friend, I think it's time to bring it to a professional. We've gone over the cheap and easy stuff first. That starter is a real PIA to even get to.