Requesting money is just that, requesting money. You input the user's email, put the amount of money you're requesting, click send, and PayPal will send them an email saying that you want x amount of money from them.
I have to manually accept the request and have the cash available.
It's not like a loan, the other person has to have the cash in their account or bank (if it's linked to the account), and then they have to accept the request. Only then will the money be sent.
They have to respond to the money request. They can respond by paying up the amount you requested, or declining / ignoring it. Obviously when you request money, you're not automatically going to get it from them.
They don't have to register an account. You can pay through PayPal with using just your card details and they can act simply as a gateway. Should they pay via card and they do have insufficient funds available then they will either enter arranged over-draft or their bank will throw a wobbly. If they have a PayPal account, they can use what funds they have available before their attached card/bank details are used.