Anyone can use PayPal without being a non-profit to ask for donations.
Yes, but there's a catch for nonprofits. From PayPal:
Note: This button is intended for fundraising. If you are not raising money for a cause, please choose another option. Nonprofits must verify their status to withdraw donations they receive. Users that are not verified nonprofits must demonstrate how their donations will be used, once they raise more than $10,000.