“What Hetter is there, in Shas or Poskim, for Yeshiva Bochurim to not daven a proper Chazaras HaShatz by Mincha”
I don’t have any idea what you’re talking about. Litvish Yeshiva bochrim are notorious for davening dramatically long shmoneh esreis.
“What’s the Maaseh with Brisk and fasting”
I’ve only heard that in regards to JB Soleveitchik. He does not represent Brisk despite his yichus. Also, I don’t know if it’s true.
“What’s the deal with shaving? Yes, I know that most Litvishe Poskim are Mattir, but there are places which say that it’s Assur.”
You clearly have your answer. You want us to be choshesh for every opinion we don’t hold by? You guys most certainly aren’t; why should we be? We hold it’s mutar, so we shave.