"I have a little money."
Translation:मेरे पास थोड़े पैसे हैं।
पास is definitely needed when you are talking about tangible possessions like money. The sentence sounds very unnatural if you omit it.
You omit पास when the possessions are abstract or intangible (like 'having a question'). It is also omitted for relatives that you 'possess' only in a figurative sense.
Yes. It is the plural of पैसा. Though it's commonly used as a general term for money, it is actually a currency unit (a hundredth of a rupee) which makes it a countable noun. In fact, रुपया (rupee) can also be used as a general word for money though less commonly than पैसा.