A second mortgage is a mortgage taken out after you already have a mortgage. The term "second" indicates the position this mortgage falls on the deed to the house.
For FHA mortgages orginated after June 2013, mortgage insurance stays on the mortgage for the life of the mortgage. Except if you put 10%+ down payment when you orginated the mortgage, then mortgage insurance drops off after year 11.
Yes, the lack of W2 income does not equate a dead end for the mortgage application process. Applying for a home mortgage without W2 income might require more documentation