Out of curiousity, is it possible to write a regex, which checks if other regexs are valid.
No, it is not possible: regular expression execution model is not powerful enough for that.
In order for a regular expression string to be valid, all parentheses in the string must be balanced. Since it is not theoretically possible to write a regular expression to verify if all parentheses in a string are balanced, it is also not possible to write a regular expression to check validity of a regular expression string.