I would say No, with the cost of a refi and also you may not have the equity in your house anymore/ou will need an appraisal completed and that will run between 300-400 dollars. I would think it will some time before a refi would be feasable.
To answer your second question, you'll need a new appraisal. Appraisals were good for six months in the past but with the most of the nation suffering from declining markets (some areas more than others), appraisals older than four months may not be allowed soon (in some areas that may already be the case). That doesn't mean the old one can't be used as a reference, it's usually good to provide a copy of it if you have it.
Since you currently have a FHA loan, doing a rate/term refinance for you would be fairly easy. Rates at this time are also much better than they were in June. I have the ability to protect pricing overnight which also means I can protect pricing during a holiday and over the weekend as well. Currently the market has improved significantly for what could be a very short window. Back in January we had a window much like the one we're currently in. It lasted for about four hours (the really good window of opportunity), the entire length of time things were fantastic for refinances was only a couple days (rates quickly shot up to the mid/upper 6's shortly after).
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If you need to call me immediately, you can find my cell on my website.