The two most common mortgage types are fixed rate, and adjustable rate.
On a fixed rate mortgage, the interest rate remains the same for the duration of the mortgage term. On an adjustable rate mortgage, the interest rate will change as markets fluctuate.
In almost every case, some down payment will be necessary, though the amount will be different for each person.
Refinancing is basically like getting a new loan on a property that you already own and already has a mortgage on it. The refinancing will change the terms of the existing loan based on the market conditions which prevail at the time.
You should always stay current with what interest rates are. If the current rates are lower than the rate you have on your loan, you should look into the prospect of refinancing.
Typically, loans are 10 year, 15 year, or 30 year.