You should start coding right away. I expect the extra experience will also help you with your degree. The important thing is to start small, and finish projects.
This is not correct, the sooner you start coding games the better! The only thing you need is a game engine (I'll put in another vote for Unity) and tutorials. Just like anything else, you just need to put the time in and the skills with come with time.
Plus there are zillions of tutorials out there. I even teach 10 year olds(seriously, part of my job) how to make games with professional development tools so it isn't that hard, at least at the start