Bank has offered without solicitation to modify my homeloan which is now variable and floating. They offered to modify at 5%. Would I be better off refinancing? Should this be doen via another institution?
Carlos, I assume your floating rate is tied to the 1 year Libor and should be about 3.25%. To answer your questions is it depends how long you plan on staying in the property and if your income allows you to refinance and there is equity in the home. Assuming there is no equity in the home or your income is...

is it possible to have 16 derogatory on credit report , all medical and get refinance
Depends on your credit score.

how fast can we get approved for an FHA Loan in Southern CA?
We can close FHA loan in 14 days typically Loan City Home Loans.