You would be starting with the principal balance you have now, and paying the rest of it down quicker. But that would only make sense if you can get a lower interest rate, factoring in all closing costs. So you have to compare making extra payments on your existing loan to pay down principal faster (end existing loan early) vs. total amount for closing costs and payments to refi. You also have to consider whether you want to be locked into higher payments (refi), or just pay extra principal when you have extra money (existing loan).

When I bought my home with 30 year mortgage in 2002 and refi’d down to 20 years in 2005 at lower interest, it chopped 7 years off of my original loan, saving saving $62,000 of interest, for an extra $30/month.

No. You would have been paying higher amounts to cut into the principle if it had been a 15 year to start with. As is, you didn’t pay that.

No, you won’t get anything back unless you have an escrow account with a balance. But that would probably roll over to the new lender’s escrow account for you.