That's not a URL.






Load one of your webpages in your browser, whatever you see in the address bar is what you've already chosen to use on your site, so..., do the same with external backlinks.

There's no right or wrong (www vs non-www), you simply pick one & stick with it. Do a 301 redirect for whichever version (www or non-www) your not using to the version your using.

The last 2 are both correct. The www option is determined by how you set up your website originally at your host provider and with your domain registrar you want to make sure they both point to the same site.
Just testing it should tell you. Not all registrars are the same.

I generally set up sites without the www, a few letters less to have to deal with.

As for backlinks, you always want to use the http to be sure that the links are picked up every time positively, and for the sake of consistency, if your site comes up as http://www.site.com then I would always use that link.

Shouldn't matter to search engines but consistency is good.

www.site.com doesn't always work. This is the short answer.
Cheers

I recommended
www.site.com
http://www.site.com