How would I create profiles for a couple of users?

The best thing to do is to create a Windows profile for each one. This way each one will have its own profile for (almost) any software installed.

When I close the browser, will that log me out of everything?

Nope, unless the pages/sites do it themselves.

Is it possible to have multiple site logins, such as two people logged into Facebook?

At a same time you can have one user logged in using the standard windows and another using the private window.

How would I create profiles for a couple of users?

Same way you do in Chrome. Just find a guide for Chrome that explains it and that will work. If you try and search for the way Opera does it you'll most likely get a lot of older results for Opera 12 and before and those guides wont apply.

When I close the browser, will that log me out of everything?

Yes. You can set things to log you back in automatically when you return to the page though.

Is it possible to have multiple site logins, such as two people logged into Facebook?

You can have up to two inside the same web browser, yes. Log into one account with the standard window and log into the other inside a private window. If you want more than that you will have to have multiple installs of Opera running simultaneously.