Hello Mark, and welcome to GameDev!
1) I'm a college student myself, so I'd like to address a few things that you might be a little misled about. I'm currently in my junior year at university, and I've only now made a solid decision on what majors/minors/etc. I'm going to graduate with. You've got time to try some things out, so don't stress too much about making the perfect decision now! But having passions and a rough idea of what you might want is a great, great idea. College needs more students like that.
On top of that, don't be worried about free time in college. There's tons of it, lying everywhere around you. I take 2 students worth of classes (the usual is 3-4 classes, and I take at least 6), work over 20 hours a week to pay for college (outside of loans), I'm a part of a social club, and engineering club, and a game programming club. The social club takes no real time; the engineering club I'm making control systems and electronics for a UAV, and the game programming club I'm making a game. This game -- alone yes (at least while I make the engine), but many people to help me out along the way.
This sounds like a lot, but seriously -- I still have time to hang out, sleep, have a social life, and relax. I'm not saying do what I do but, whatever workload you have, you can make it work. Most places have gamedev clubs and such -- use those!! You can find the time to do the things you want -- like make games and a portfolio, if this is what you want to do -- if it's what you want and you have the passion for it (and a little bit of skill, and luck!).
When applying to internships, current projects are HUGE!!!!!! I've nailed so many internships talking about the project's I've done and showing off physical results and companies love that. If you have experience, that's worth a ton to a company -- you are more versed in how things go, and you've seen with your senses, exactly how things work and how things go wrong. I've been accepted to an internship because of a project I failed -- and failed as in a UAV turned into a flying flame-ball of death -- but the company saw the experience I gained, especially from the mishap, and how careful and how meticulous my planning is when working on future projects. All in all: experience is key.
2) I don't know much about this because I've only had internships and jobs as an engineer, but I've seen that people like seeing that you have knowledge of a lot, and can handle that, but really are phenomenal at one or two specific topics. It shows that you can learn quickly and retain knowledge, while you can also become an expert in things that need to be done by you, too.
3) I don't know
4) I'd say the internship programs are best. I've had friends go through the program at Blizzard, and they loved it and learned a crazy amount of amazing things during their time there.
5) Got no experience here either, sorry!
I hope this helped. Sorry for the wall of text! I hope the college perspective can help you understand things and show you'll have plenty of free time