I read in news reports that people with "paychecks" will receive a rebate, assuming the proposal goes through.

Does with "paychecks" mean that people who file Schedule C (income from business), and not - what is it? - W2s, will receive nothing?

It will be based upon your 1040 net income, so if you write off lots, it could be less. There will also be a diminishing amount for both small and large earners.