Do You Have To Have A Credit Card To Receive Money On Paypal?

Go to http://www.paypal.com and set up your own account. You do not have to have a credit card to do this, however you will need a valid and functioning bank account. You will also have to provide PayPal with adequate identification and what purpose you will be using the account for.
I am not sure if I understand your part of the question about accepting donations. If you mean can you accept money for a charitable organization, then the answer is no you cannot. Only authorized representatives of a charitable organization may accept donations for that organization. If you wish to solicit donations for a charitable organization you may do this as long as PayPal is not involved, and, this is very important, you request that the donations be sent DIRECTLY to the charitable organization. Otherwise you are in danger of breaking several state and federal laws. You could be arrested, fined, and imprisoned for representing yourself as an authorized person to accept donations for a charitable organization.
To become an authorized representative for a charitable organization, contact that organization directly and ask them for details on how to raise funds for them.