If I baby-sit/nanny and make over $400.00 in a year, at age 21, am I required to pay self-employment, state, federal, soc. sec. etc. taxes? (I am a full-time student)

You are self employed or independent contractor.

You will report your income and expenses on schedule C or C-EZ (Form 1040). Then you put net income (or loss) on line 12 of Form 1040. This income is subject to SE tax at 15.3% (this is shown on line 57 of Form 1040). Half of SE tax is deductible on line 27 of Form 1040. Read: Your U.S. Tax Return: Tax Filing by Self Employed Sole Proprietor or Independent Contractor