I am also in university, have good grades and stutter like a motherfucker. Sure i try to cure myself with different methods, even unusual ones and some of them kinda help, but stutter is still there and sometimes gets pretty strong too where I can’t even put my words together in a short amount of time. This god damn life is hard with stutter, I know how you feel. The first problem with your post I see is that you are trying to prove people that you are not dumb. Why would you do that, fuck them. Keep studying and evolving. The only person you need to prove anything is yourself. When people laugh at you then just laugh with them, sometimes my weird faces and non ability to say words in short time are even funny for me, don’t be too defensive if you want to have people around. Start joking about stuttering and people will want to spend more time with you. The break of eye contact is very normal, don’t worry about it. When humans communicate the eyes will start to wander, it is just human psychology. Even when people without stutter communicate they don’t stare at each other all the time, that would be just creepy.