What do I do with dependent care expenses that I pay THIS year but are for NEXT year? Do I file them THIS year or NEXT year? (Example: Paying for a Spring camp in Dec).

You claim the prepaid expenses next year. The following is from IRS Publication 503.

"Expenses prepaid in an earlier year. If you pay for services before they are provided, you can count the prepaid expenses only in the year the care is received. Claim the expenses for the later year as if they were actually paid in that later year."

and be sure to read Pub 503 for what expenses qualify.  for example summer camp qualifies only if it is day camp.  overnight camp doesn't.