If I go out to the shops and buy myself some pencils with my own money, does my mom have the right to throw the pencils in the trash?

i dont think so

From what I recall there are legal issues, you are a legal adult, she is your guardian.  From reading your questions I assume you should not be "around" sharp objects, including pencils.  So, yes, she has the right.

sounds like you left them lying around after she told you to put them away

Legally yes she can as she is your legal guardian

She's just mad buz you were supposed to buy a new helmet, Rainman.

Well, it depends. Your mom has no right to do that if you earned that money. If that money was earned by working a job. If that money was given TO you by your mom, then its technically her money.

Your “own” money comes from the pocket money your mom gave you, am I right kid?