Can a boolean be also open/closed?

Answer 1

Yes. A boolean can represent anything that has only 2 different states.

var open = true;
open = false; //closed

Answer 2

You will only be able to compare open/closed as boolean if you declare both an open and closed variable

var open = true,
closed = false;

if (open)
{
document.write('open');
}

If you don't declare the variables, open will be undefined

Answer 3

yes ,of course.