Can one donate a percentage of one's income yearly to non-profits and charities? Is this acceptable by the IRS?

The IRS could care less about how much you give to 501(c)3 charities or bona fide religious organizations.  What they care about is how much you deduct as an itemized deduction.  There are limitations depending on the type of gift and you cannot deduct total donations exceeding 50% of your income.  If you make donations exceeding the limit, you can carry them forward to use the next year.  Review the instructions for Form 1040 Schedule A at www.irs.gov