Hey Servadac,
You are a chatty fellow! I like that, it is much easier to learn when you read and ask.
Let me answer a few of your questions.
There are numerous icons on the forum. Some are for certain grows, for example, my Dutch Passion icon was earned from completing a documented Dutch Passion grow on the forum. Sweet Seeds, High Rise, Dragon, Flash, I know I am leaving someone out, also has them as well. Once you have completed a grow journal, shoot the forum mod a PM and they will hook you up with your icon. As for the High Team, that is a service icon just like Moderator and such. We on the High Team are responsible for greeting new members, helping people find the correct places to post and generally spreading overall good vibes on the forum. We are picked by the mods to do the job.
The rep you were asking about it correct. Generally you receive "rep" for one of the following. Completing a grow journal, helping a fellow member, completing a smoke report, reviewing an item you have, etc. There are many ways to get rep and most of them have to do with helping our community. The more rep you receive, the more you are able to give. Also, your little description below your name that says "Novice" will change as you receive rep. There is also a set of green bars under that, the more posts you have, the higher the bar level goes but that has nothing to do with rep.
Hopefully that has helped you understand the community a little better! One more thing, if you click the little Settings button at the top right of the screen, you will be taken to a page that shows who has given you rep, a small reason for their rep, and a link to the thread that they repped you on. It is normally in good taste to go to that member's profile and leave a kind message on their "wall" after a rep has been received.
Best of luck on the forum bud!