Will being listed as a dependent on my parent's tax form decrease my tax return?

The IRS allows you a personal deduction against taxable income which you will lose if your parents claim you. The loss of the deduction will increase your tax and thereby reduce your refund.

If a family member pays me to do work for them, is it taxable?

A contractor reports self-employment income and expenses on a Schedule "C" Form 1040. That income includes money received from family members for contracting work performed.