1. in terms of business: you need first to register in your local area as a self employed business. Talk to your council about that. Then you'll need a food hygiene certificate Level 2. If you want to start your business from home it'll be harder unless you have 2 kitchens, 1 for your business, but it can be done Obviously if you have pets or young children you'll need to make sure it is clean without hairs, etc. Then, when you're just about ready to open, you'll need to get a visit (arranged by council) from your enviromental health officer. They will give you the all clear.
you may also want public/customer liability insurance :)
2. Businesses are expensive. I would suggest doing it from home since you're so young. get a parent or 18+ to be your partner and sign everything - a parent is better as then they can sign in your name and it can be your business. As youre young a home business should be okay because unless you can afford a good website and good advertising, you wont be overloaded with customers and therefore it wont be impossible, especially if you have someone helping you.
3. Stick to making cupcakes as custom orders rather than distributing them. Have a flyer to give to friends and a page on facebook where you say you need 1 or 2 days notice and can make batches of so many in such and such flavours, but can do custom flavours at a price. Remember to say you Bake on Order.
4. Name: Something clever that reflects your company.
Sophisticated - CakeCentral, CupcakeCentral, CherryOnToppe, ThePatisserie,
Fun and cute - CakeCentral, SweetThings, Cupcake Fairy, Batter It Up, BatteredFairy, CupcakesWithWings, etc, think fairy themed and ingredient themed...or even *yourname* cupcakes