Can I start a web design business in high school?

I am a high school student, and I really want to make some money to help my family and myself. I would go the normal route and try to get a day job while in school or work during the summer, but I attend a boarding school and so a day job is not an option. I want to begin working now and not limit myself to the summer. My main, and most marketable, skill is my programming ability, so I think I could do well with web design. Because of my age, I'm ineligible for a number of freelance sites, so here's my question: Can I start a web design business from the dorm, or is this something that requires face-to-face contact with clients? Is it even reasonable or legal to try something like this at my age? any advice would be greatly appreciated.



Bonus question: Should I be paying for/setting up my client's hosting/domain name or should I just design the website (html files, resources, etc) and leave finding/paying for a domain and hosting to them?



Startup steps that I have plenned so far are:

1. Design my own website to show to potential clients

2. Find a couple of jobs, offer them for a lower than usual price or free to build up a portfolio

3. Add those sites to my portfolio, ask for referrals, up price, get more clients

4. Continue?