Under "Deductions Related to Foreign Earned Income" - should the amounts entered be negative or positive?

They are asking for the deduction amount so you would enter any deductions as a positive number.

When I enter it as a positive number, my tax liabilities (tax I owe) increase instead of decreasing. But when I enter it as a negative number my tax liabilities decrease, which make sense. Is this a glitch in TurboTax?

The deduction from foreign earned income gives you less income to exclude so your tax would increase.  TurboTax is calculating it correctly.