No — this calculates the pure loan principal-and-interest payment. Mortgages in particular often have additional costs (property tax, insurance, mortgage insurance) added to the monthly bill that aren't included here.
This calculator assumes a fixed rate for the full term. For an adjustable-rate loan, run the calculation again with the new rate and remaining balance/term once the rate changes.
In standard amortization, interest is calculated on the remaining balance each month, which is largest at the start. As the balance shrinks, more of each equal payment goes toward principal — this is normal and not a sign of a bad loan.