Is there a limit on income from rentals or fund raisers to keep the 501(C) (3).

I don't believe a 501(c)(3) organization pays taxes. Keeping the 501(c)(3) designation involves proving that you are or a supporting a charitable organization. You are required to file financial statements annually so your status can be reviewed. If its found that you are raising money and not disbursing it or using it improperly, you will lose the 501(c)(3).

Any income that does not come from donations or income not related to charity work is taxable. For example if our church bought and owned a shopping mall, we would have to pay taxes on any of that income

That is how our accountant has explained it in laymen terms to me