Let's explain the levels a bit more:
-Bronze is:
basic patterns,
1-3 years of dancing is expected
Technique is most important, since there isn't a whole lot that you can do.
-Silver is more advanced
allowing more patterns
3-10 years
technique is important, but so is interpreting the music
-Gold is the top of the line
Really no limit on patterns
"Hobby-ist" is the term I hear a lot
Music interpretation is extremely important
We joke that it's more important to stand there and look good, than doing the actual dance patterns.
Closed vs Gold. I don't know what that means in Gold, but for Bronze and Silver, Closed means "must stay within that level's syllabus". Open means you can bump it up a notch (e.g., You can do a lower silver pattern in open bronze).
As for going Professional, all it takes is giving lessons and getting paid for it. I've seen 18 yr old dance instructors, but if you are planning on doing the college dance club, I believe you have to have amateur status. Some of the best dancers I know are amateur-amateur partnerships. And they have recently changed the rules that if you win enough championships (double-check w/ USABDA, please) you can sell lessons. But you're young, and heading to college save that decision for later.
One thing I know about Gold levels, is that there isn't that many people who compete in it, especially in A1 (18- to approx 35ish years old) on a Pro/Am level. So you might not have any competition, if it's a small enough comp. That may or may not be important to you, personally I prefer having competition, makes the money and the placement seem worth it. Best bet is to find someone who has the program to whatever Competition you are planning on attending and find out what last year's entries were.
Does your instructor have a student already dancing A1-latin-silver?
oopps gotta go. good luck.