Hello, my name is Andrew and I am a 17 year old young man from California (will be turning 18 on August 5th). I have a few questions concerning New Hampshire and any help I can get would be appreciated. 
Welcome, Andrew.

1. I am going to be a politician when I become older and was wondering what the age and citizenship requirements are for participation in New Hampshire's state legislative and executive offices. How old do I have to be and how long do I have to be a citizen of New Hampshire?
2. Also, I would be very interested to know what town does not have a liberty-minded representative in the state legislature. No point in running one of us against another, so I'd rather be informed of what areas need a libertarian representative and then I will move there and run against the incumbent as soon as I can. I will most likely be registered as a Republican.
The NHLiberty links Denis provided should help you answer those questions.
3. As a young man, I will not be able to afford much in the way of housing. Are there affordable places to live in New Hampshire? Here in California it's impossible to live within one's means. Debt abounds and I am not about to participate in the culture of borrowing and false wealth that permeates contemporary society. It is my desire to avoid debt wherever possible, and if affordable housing can be found in New Hampshire (preferably I will be rooming with a few others or something) then it will greatly influence my decision to go there.
Housing in NH isn't "cheap" necessarily, but it might be cheap relative to what you're used to in CA. The reason it's not cheap in NH is because a big percentage of tax revenue comes from property taxes. No income tax, no general sales tax. So remember that if you pay a little more in rent/property taxes, you'll likely more than make up for it by not being taxed on your income or things you buy. Anyway, there are a few places where porcs can go to rent from a porc and live as roomates/housemates with other porcs:
www.porcmanor.com4. I am a great public speaker and writer (no need to be modest here
), and am very interested in taking part in the revolution on a vocal and literary level. Are there organizations, groups, etc. within New Hampshire interested in employing the talents of someone my age in the fight for freedom?
There are at least 2 liberty-oriented newspapers in the state that I'm aware of. One in Keene (
www.keenefreepress.com), and I think one in Manchester (not sure of the name). Hopefully someone else can chime in. There's also Free Talk Live, a radio show based out of Keene. And there may be other liberty media outlets that could use a good speaker/writer. It might take a little research and some further questioning.
Meanwhile, I suggest you move to Manchester, get a room at Manchester's Porc Manor, and practice your speeches at Murhpy's Taproom (
www.murphystaproom.net) -- though you'll have to wait a few years to legally enjoy the excellent beers on tap.
5. What is there in the way of college education in New Hampshire? Any place affordable; any place recognized? Any place to major specifically in law and economics?
Not sure what you mean by recognized. If you mean "prestigious", then look into Dartmouth. As in ivy-league prestigious. And probably expensive, unless you get a good scholarship. UNH (
www.unh.edu) is more affordable, and less prestigious than Dartmouth. It's a good school, and I'm sure you can major in economics/pre-law.
6. And last, but certainly not least, can I find people to get wine for me if I so desire it? 
You're on your own there, sorry.
