1. Would most likely need to document your mortgage history with cancelled checks.
2. As an investment property you would most likely need 20% equity to accomplish the refinance. Though you would not need this much as a primary residence.
3. I can not currently check the Approval status of the project, though it will most likely need to already be approved, though some lenders may be able to offer a spot approval.
4. In regards to purchasing a new property, you most likely need to have 30% equity in your existing property unless you can qualify for the new payment on top of your existing payment. That is the equity is required if you need the rental income to make your debt ratios acceptable.
There may be some portfolio options depending on other factors which would not be subject to the same requirements that most lenders offer. Smaller banks can generally write loans that are outside of the box, though generally come at a higher cost.