1) Yes, sort of. A "Normal" expression would be anything that results in a value, like (x + 4) / 3
or sqrt(25)
. A Regular Expression is something different, though.
2) An expression is usually the right-hand side of an assignment statement or part of a conditional. A Regular Expression is something different, though.
3) Because someone named it that. ;) It doesn't have much to do with a mathematical expression or a normal programming expression AFAIK.
4) Depending on the language, it's a regex because of the syntax. For example in javascript, you know a regex when you see one, because either the regex literal syntax is used, ie. var re = /.*/g;
or the RegExp constructor is used, ie. var re = new RegExp('/.*/', 'g')
5) Nope.
edit:
I've been informed that my answer for #3 is incorrect... It's called a regular expression because it's meant to parse regular languages, which tie in closely with computater science and mathematics.