But to be honest - my proveable income is low. But my credit report history is excellent. So that is why I am wondering how to get a mortgage without them asking for evidence of income.
For a loan with no income verification, your options are 1) hard/private money, 2) portfolio loans, or 3) seller financing.
For hard money or private money the interest starts at 8% plus origination points; these loans are meant to be short term. For someone will no experience, interest can be significantly higher (12%+). Some banks will do portfolio loans that are only based off the property income but they are looking for people with experience in the industry.
Seller financing may be your only option at this point; the vast majority of sellers will not be interested and interest rates are higher than conventional mortgages but usually lower than hard/private money. Amortization and payment terms can vary widely.
Regarding the sample property, you left out a few things.
Rent: $1,200
Costs: /mo
P&I (25% down, 4.75%): $587
T&I (guess $700/yr insurance): $116
Repairs (10% rent): $120
Vacancy (10%): $120
CapEx (10%) $120
Management (10% even if it's you): $120
Net: $17/mo