Is it possible to use paypal for things like paying a speeding ticket from Italy and making a deposit on a hotel stay in Croatia? I have their account numbers. Thanks!

If you are paying the fine direct to the Italian authorities (police, for example), it seems unlikely they have a paypal account. Usually a fine can only be paid into their bank account, quoted on the covering letter. If you are reimbursing the fine paid on your behalf by the rental company (plus admin charge), you can probably pay by credit card.
Whether you can pay a hotelier in Croatia again depends if they have a paypal account. If not, direct transfer into their bank account or credit card seem other options.