Yes,
When you open an account at a bank, you are essentially entering in to a contract to do business with that bank. In the U.S., you need to be 18 to legally enter in to a contract.
The only other alternative is to have a parent go with you and they would become a guardian of the account and let you be a joint or co owner. But I have no idea if Wells Fargo alows that.
As far asthe ATM fees go, I usually spend less than $10.00 per month and then I even get that reimbursed by my bank.
1. Use your debit card instead of cash.
2. Pull more than $10 or $20 out at a time.