Yes, you can file a charge back on a credit card payment any time that you use your card without actually signing your name to the purchase.
No I'm unsure if providers all offer the same time period as to when a charge back has to be claimed by, but the standard time is around 2-3 months from what I have heard.
Contact your card provider to get full charge back details.
To be honest, using your credit card for purchases is about the best form of payment. While PayPal does offer some level of protection, it's not as much as the charge back system on a credit card.