If something says "pay with paypal" does that mean I can, like on ebay, use a credit card through paypal?

yes, go to www.paypal.com for access

Yes, I think so. I've paid for something on a non-eBay site that way, and when I clicked on the link, it took me to PayPal, and I could use my credit card or whatever other means at that point.

No but a creditor can send you a PayPal invoice that you can pay with a credit card and not have an account.