1. How sweaty you would get depends on how warm it is and how hard you're working. Riding slower means you would sweat less but if it's hot out, you have a long way to ride or you have big hills to climb you might get sweaty even if you're riding relatively slowly.

2. This is related to #1 . Generally you work as hard as you want to, but long steep hills are going to be hard regardless. The distances you mention don't seem too bad. If you're athletic I don't think you'd find riding a bike to be very hard, especially after you got used to it.

3. If the roads are smooth you have lots of options but it still depends on how much you want/need to carry with you and again, hills. A lot is just personal preference, especially when it comes to shorter distances. You don't mention whether you male or female. The only reason I mention that is a 14.5 year old girl may not get a lot taller where a 14.5 boy still has some growing to do. I wouldn't spend a ton of money on a bike that may not fit you in 2 years.

By the way, I've seen people in Hawaii ride with surfboards mounted to their bikes.