Thanks for all of your answers
I was a bit winded up when I posted this one, I had just spent all of my savings on our band's website (which in my opinion wasn't necessary) and so on...
Actually, did work on summer and also do house chores now, but do not ask money for it, in my opinion a bit wrong to ask money from parents, when what you do at home you do to make your living comfortable and enjoyable for yourself (hope you get the idea)
Drum stuff I'm looking for is heads and sticks mostly, because they come and go. Of course parents sponsor me sticks sometimes, but that's about it. Also sometimes the urge to have many things comes up and then I'm like "oh, I need this and that", kind of annoying.
You sound very level-headed. Here is my take on it:
Of course you do chores at home for no pay. It's a part of being a contributing member of your family. If you get paid for jobs or an allowance, that's between you and your parents.
When looking for "jobs" (which are more than just a summer thing...spring time is when people need help planting, summertime is when people maintain their yards and work on their houses, fall is when people do most of their raking, etc...you can find work any time of year, not just summer!), ask your neighbors. Especially people who are further along in their years. They need the most help, will be the most willing to ask for help, and usually have the most means with which to pay you, and they're glad to.
YOU paid for your band's website? Live and learn. EVERYONE in the band should chip in. At this point, while you're in school, you don't need a website unless you are actively promoting your group and getting gigs. Even so, if the other members don't want to contribute to the band fund or website costs, then it's not important enough to them, and you should either let it slide or get new members in your group who have the same vision as you.
About the saving money thing, you should get into the habit of stashing away money now while you're young. Don't live at the edge of your means, or spend all of your extra money. Get in the habit of saving now. It will be an asset to you later on in life. I'm teaching my young kids right now that they need to stash/save at least 30% of the money they get. When you get $10, don't think of it as, "Yay! I have $10!" Think of it more along the lines of, "Yay! I have $5 to spend, $2 to put towards drum equipment, and $3 to save long-term for college/car/house payment/retirement/whatever."
Lastly, if you're really passionate about drumming, and your parents are supportive, I would see no reason why they wouldn't spring for the occasional new heads or sticks, especially if you're keeping up at school and around the house. It's one thing to be all like, "Hey, mom and pop, can I have ANOTHER new set of cymbals? The set you bought me last month are boring me now, and so is that Black Beauty snare...I need something new, and I need it now, now, now, waaaaah!". And, it's another thing to approach your parents about how your tom heads are wearing out, or the coating on your snare head doesn't allow you to practice brushes effectively, and so forth.
...there's my $0.02, pushed in your face. Take it or leave it.