Interesting discussion. Here's my response.

Answer to question 1
I have a computer science degree and an electrical engineering degree. Going through uni gave me self-confidence. My programming skill as such has not improved much in my uni days, but I have learnt so much on machine architecture, algorithm, efficiency, database theory, AI, etc. that I have helped me tremendously in my work.

Answer to question 2
As far as I am concerned, I don't think having a degree in computer science matters that much. Many of my colleagues have degrees in Maths and Physics, Aerospace Engineering, etc. I would rather call myself a software engineer. I were given more preference because I have two degrees and a strong engineering background (especially useful when working in a larger group), but most importantly because of my business knowledge, work experience and my programming skills.

The conclusion
Much to learn I have (Voice of master Yoda echos in my head). University only showed me the path, I have to actually walk it.