Is it possible to setup a Paypal account with no credit-card?: Yes
And if so does it work in all countries?: Canadian Premier paypal's work the best.
Is there a way I can put in fake information?: use FakeNameGenerator.com ; but if you get limited, gg to you.
It is possible to register without a back account but this will leave you un verified and most sites won't allow un verified users to purchase from them, I know you can get virtual credit cards (VCC) so just do some research