For example, if my salary is $60,000, and I receive $12,000 in rental income (12 months of $1,000 in rent.. of course this number does not include deductions like repairs, taxes, interest, etc), does that mean the government will consider my gross income to be $72,000 when deciding if I qualify for the stimulus checks? I think gross income of $75,000 or less for single filers qualifies for the full amount
Yes, assuming you are a sole proprietorship or LLC your net income will flow through to you as standard income. You are taking depreciation though, right? That will shelter some portion of that additional income.