does ebay only allow buyers to pay with paypal?

Depends on the person selling the item. Some will take checks, money orders, etc.

Yes they do, that's there preferred method of payment, paypal is also owned by ebay.

It's easier to do with Paypal, but a credit card will work.

mostly yes and it is safer

Most people will want you to buy with paypal. It's the easiest, fastest and most reliable transaction. I would highly recommend paying only with paypal. But the short answer to your question would just be no.

Most sellers prefer PayPal. eBay itself prefers PayPal. Some sellers don't like it though. So I avoid them.

On ebay in the U.S., the seller is no longer allowed to advertise if they accept alternate forms of payment besides paypal ( ebay owns paypal). However, many sellers will accept alternate forms of payment such as check, money order, cash, etc. The buyer now has to ask the seller if they accept these other forms of payment. This rule is a few months old now.