I'm not experienced with servers, and I'm curious. Sorry if I mix everything.

I understand that a private server is mandatory when you want to play with friends.

1. Are passwords really required if you don't invite anybody else (and you trust all of your friends), and the server stay private?
   
2. If a server is public, can someone draw by chance the same exact seed for a private server (or a solo play), and actually enters an already populated world without being invited?