rental income on non subject investment property
JD, Take the income off of Sch E, add back the depreciation, mortgage interest, taxes and insurance and subtract the PITI. Positive number goes to income, negative number goes to liabilities. Your Underwriter will decide whether your borrower will be hit for the full PITI or not.

mortgage transfer
Sorry but no.

Should I refinance my house?
Maybe you should stand pat with what you have. I don't know what your loan size is but $1000.00 at 5.12% on a 15 year mortgage is $7.97 a month. A ten year loan at 2.3% ( according to Travis) costs $9.34. . To pay off your loan in 6 years would cost $14.88 per thousand. You do the math. Multiply $14.88 times what you owe....