What do ^$ and ^# mean?

++

From What is double plus in regular expressions?

That's a Possessive Quantifier.

It basically means that if the regex engine fails matching later, it will not go back and try to undo the matches it made here. In most cases, it allows the engine to fail much faster, and can give you some control where you need it - which is very rare for most uses.

*+

*+ is the possessive quantifier for the * quantifier.