Without the 30% equity, you will be required to prove 6 months' worth of reserves for mortgage payment, property axes, home owner's insurance and association fees (if applicable) for both houses.
This is a result of FHA's and Fannie's policy to prevent "Buy & Bail" tactics by home sellers.
I am a Loan Officer. If I can be of assistance, please let me know.
2. If you have good credit, there are loans out there, FHA with 3% down is the one being used the most today, but Conventional loans can still be gotten with 5-10% down, you will need good credit and reserves though. Both conventional anf FHA have good current market rates so rate shouldnt be a problem with your good credit.
3. The rental question, if you rent you current home you will have the payment counted against your income, BUT 75% of the rental income will be added back to your income to help of set the payment.
Good luck with your move!
Nations Funding Source, Inc
Nationwide FHA, VA and Conventional Lending