Do business expenses reduce earned income? Can I make a Roth IRA contribution if earned income is over 5500 but expenses are greater than earned income?

Yes business expenses DO reduce earned income.  Your earned income is the Net Profit on schedule C minus half of the self employment tax on the profit.  So actually it's a little less than the Net Profit.  If you have a Net Loss it doesn't count at all for earned income and I think will even reduce earned income from any W2 wages you might have.

and remember that you are required to claim all of your business expenses.