The questions you ask are good ones, But they are multifaceted. Lets start with can there be a student with out a instructor. Absolutally although some may disagree its sort of the chicken or the egg arguement. How ever it can make things far more difficult. Martial Arts, well let me rephrase that Martial Science like JKD is not simply about moves, its about using those moves to maximum effectiveness.
Next question is this normal. You have the exuberance of youth, something I'm sure all of us here will tell you is a good thing, for you there is no bondries to what you can do. Just be sure that you dont push to hard to fast. One can not expect to go from 0 to 60 instantly, not even bruce could do that at first.
My recomendation to you, is to get a good solid base in the martial arts, JKD, Karate, Kung Fu, Several systems, but at the same time make it your teaching goal be your end result. Feel free to visit the local dojo, talk to the Sensei or Sifu about your goals and how in your situation he would think is the best way to achieve them.
If he seems null and try's to steer you away from what you think is important be firm but polite (ALWAYS POLITE RESPECT) and just ask him where this would lead if you dont see the point right away.
Also Book reading is good, historical reading, I dunno thats just me I'm heavy into tradition I know bruce wasnt when it came to JKD.
My Final and Last Peice of advice to you is two things, STAY in school all the way through college even when you see your goal in site finish school, It can be very difficult to make a living at martial arts, ecspeically with the economy being in the ****ter. Its good to have something to fall back on. Maybe even something related. Bruce him self was a very schollarly gentlemen who from what I understand prized knowlege.
Second if you need any pointers teachers to call people things like that feel free to post here and email me if you like Ive got names and reference books up the wazzu.
I hope I was of Help
PS Your enthuzansm is infectios Keep it up Good luck