I am in the EXACT same position as you, with a similar degree, so so frustrating. But I cannot only blame it on my stutter, in general, I am just bad at speaking and being put on the spot despite the amount of preparation I put in. What I can say though is that these other problems are a long term effect of having a stammer. I just get really anxious and nervy especially when the interview is in front of >1 person. I tend to forget a bunch of my answers & when put on the spot, I often do not have an answer. I struggle with competency questions the most due to a lack of examples... which is because I lack the experience... which is because I was never good enough to pass interviews for placements/internships etc. It is literally a never-ending cycle.