How much can stock turbo handle.
 

I have an 05 wrx with turbo back, Typhoon intake, and I want to get the hullman boost controller. I want to keep stock turbo for now, How much can I boost the stock turbo with the apprpriate tune??

If you want your engine to be reliable like you said you'll need to tune it. Get new injectors, and a fuel pump. You'll probably need new internals as us wrx's dont get forged pistons like the STI's do. With all that you could run pretty high boost, about 19lbs. If you dont get all that than you can safely raise it a few pounds or so, not too much because of reliability issues.

from everything I have heard and read -1 for boost controller with stock turbo.

I'm running 1.3 bar or ~ 21 PSI on stock internals on my '02 WRX. However, I'm not running it on a stock turbo because you won't get any more power by boosting at higher than stock levels. IIRC, the stock turbo boosts around 1 bar or ~ 14 PSI and anything after that it just blows hot air and won't do anything more.

I dunno if you just forgot to list it, but save up for a Up Pipe before trying to boost more.