Amortizing a loan means that you are eliminating (or paying off) the loan.
Payments are set up so that each payment is the same amount. As time goes on, the amount of each payment that goes toward interest decreases, and the amount of each payment that goes towards principal increases.
The payment gets smaller (because you are spreading out the payments over more time).
BUT, the total interest paid (and therefore the total amount paid) gets larger (because you are being charged interest over a longer period of time).
The outstanding principal is how much you have left to pay off the loan. In other words, it's how much you still owe on the loan.
Equity is the difference between the home's value and the outstanding principal
Equity = (value of home) - (outstanding principal)
You can think of "equity" as being the amount of money you'd walk away with if you sold your house. The "value of the home" is how much you could sell the house for, and the "outstanding principal" is how much you still owe on your mortgage.
A balloon payment is one big lump sum payment at the end of a loan. It is a repayment of the outstanding balance.