It depends on your current credit score, how much your new loan amount will be compared to the current market value, ect. If you recently purchased the home and financed 100% of the purchase price you may not have any equity in the home yet. If you put a good chunk of money down then you may benefit from refinancing.

If you have good credit, you could probably drop your rate .75% right now.

Perhaps. The biggest factor will probably be your credit score. If you haven't talked to several banks, I would suggest you start there. You can do some preliminary searching online. http://www.lendingtree.com is another great resource.