When you file your taxes, you only need the numbers. You aren't sending in cancelled checks and/or receipts.
In the event of a tax audit, it is up to you to prove the validity of the deduction. They start with an assumption of NOT DEDUCTIBLE, and with your documentation, the auditor and you come to agreements. Audits are not common. But, when it happens, be advised that a cancelled check is not as good a proof as a printed and signed receipt. A check shows you paid someone something, but does not show what it is really for and whether you received anything in return.
Also note, charitable deductions are an itemized item of Schedule A. There were some past years of more deductibility, but currently, it is only when itemizing that there is any need for receipt at all to have in records.
Answer is all of yes, no, and maybe at the same time to this.