It’s definitely possible to buy a vehicle when you’re licensed in a different state, but it’s a bit tricky (I bought a car in Ohio with a North Carolina license). It takes longer, and they have to send mail back and forth with your home state. One potential problem is that the MSF course is for CA, so it would get you a CA license. You would need a Virginia motorcycle license somehow (the Massachusetts permit doesn’t allow you to ride out of state, so you would need the license).
I see two basic options. You could take the MSF course in VA, get your license there, and then buy a bike. Or you could get a NY license, take the course there, etc. Since you’re just working in Cali for the summer, it doesn’t make any sense to get a Cali license. You’ll be paying CA taxes anyway, since you’re working there. And with a CA license, you’ll have to register your bike there, and pay taxes on it there, but that’s easy. The only way it would make sense to get a CA license is if you know you’re going back there after school.
What year are you in school? And do you know where you’ll end up after graduation? It costs money to transfer registration and title to a new state, so doing that as few times as possible is good.
It seems like you best option would be the see if the VA DMV recognizes an MSF from California. If not, try to get back to the east coast for a weekend to take the MSF. And if neither of those can happen, you’re probably better off waiting until the fall to get your license.
If you do get one in Cali, to get it across the country you could ride it if you’re at a point where you’re comfortable with that, or you could rent a Uhaul or something and put it in the back.
In terms of the winter, my bike will be going into storage for the Boston winter. There’s a dealership that had a deal where they drain all the fluids, put it in a climate controlled garage, hook up a battery tender, and then refill all the fluids when you come to pick it up. The price isn’t bad either. You could accomplish the same thing yourself with a cover and or something. But I won’t be riding on the ice and snow.
For music, I don’t listen to music when I ride, but I’m still a fairly new rider. I would have a problem listening to music in heavy city traffic, but on the highway or out in the “country” (doesn’t even have to be the real country), I wouldn’t have a problem with it. Check the laws. Some states say that one earpiece is ok, but not two. I treat it as a personal choice though, whatever the law says.