You are not allowed to deduct any charitable donations without proof of the donation.
If under $500 was given with a credit card, would the credit card statement count as a receipt?
What about this scenario?
The only exception is donations made to organizations that have a dropbox type operation where a receipt is impractical.
No, if the donation is over $250, then you also need written acknowledgment from the charity in order to have sufficient documentation if requested by the IRS.
For further information, take a look at the following TurboTax help article and the link to information provided by the IRS:
Do I need a receipt for my donation?
Charitable Organizations - Substantiation and Disclosure Requirements