Trever,
I've known 7 year old HAM licensees. You absolutely don't have to be over any age to take the test.
There are actually a few tests, and classes. Right now, there are three "classes" of license:
1) "Technician" - gives you mostly access to UHF and VHF, being able to talk on your local "repeaters" with handheld "walkie talkie" (though more advanced) type radios. Good for local communication, pretty easy test.
2) "General", gives you "HF" privileges, colloquially known as "shortwave" frequencies. This will allow you to talk to other countries from a desktop-type radio, up to 1500w.
3) "Extra" - gives you more HF frequencies and privileges. Harder test, but I'd look at Tech and General for now.
To get a General class license you'd have to take the Technician and General test elements. To get Extra, you'd have to take Technician and General and Extra.
CB is considered "11m HF", ~27mhz.
The closest HAM band would be "10m HF" ~28mhz.
It looks a little like this:
CB (Default privileges) 11m HF ~27mhz AM (FM in some countries), 4 watts.
========
HAM (Technician License) 23cm SHF ~1.25-1.3ghz, AM/FM/SSB/Data, 200 watts
HAM (Technician License) 33cm UHF ~900-928mhz, AM/FM/SSB/Data, 1500 Watts
HAM (Technician License) 70cm UHF ~420-450mhz, AM/FM/SSB/Data, 1500 watts
HAM (Technician License) 1.25m VHF ~222-225mhz, AM/FM/SSB/Data, 1500 watts.
HAM (Technician License) 2m VHF ~144-148mhz, AM/FM/SSB/Data, 1500 watts.
HAM (Technician License) 6m HF ~50-54mhz, AM/FM/SSB/Data, 1500 watts
HAM (General License) 10m HF ~28-29mhz AM/FM/SSB/Data, 1500 watts.
HAM (General License) 12m HF ~24-25mhz AM/FM/SSB/Data, 1500 watts.
HAM (General License) 15m HF ~21-21.5mhz AM/FM/SSB/Data, 1500 watts.
HAM (General License) 17m HF ~18mhz AM/FM/SSB/Data, 1500 watts.
HAM (General License) 20m HF ~14mhz AM/FM/SSB/Data, 1500 watts.
HAM (General License) 30m HF ~10mhz Data, 200 watts.
HAM (General License) 40m HF ~7mhz AM/FM/SSB/Data, 1500 watts.
HAM (General License) 60m HF ~5mhz USB Voice, 50 watts.
HAM (General License) 80m HF ~4mhz AM/FM/SSB/Data, 1500 watts.
HAM (General License) 160m HF ~2mhz AM/FM/SSB/Data, 1500 watts.
... So as you can see, HAM is quite a bit different than CB.
When we say "meters" we're referring to the wavelength function of frequency. It's really the same thing as when we say "405nm" here to specify the frequency for a violet laser, or "650nm" to specify red. These are just lower electromagnetic frequencies. So we say 30m, 15m, 160m, etc, in 'meters' instead of 'nanometers' to specify the band.
A good place to practice the tests is here:
AA9PW FCC Exam Practice
There are also some good books out there on it; unfortunately I think the best one is out of print now... and a good starting point is here:
Getting Licensed .
(I know a lot of older hams don't like the ARRL for various reasons; I'm trying to stay apolitical on it.)
But, hopefully this gives you an idea of it, and, at 15, there's absolutely nothing stopping you from getting into ham radio.