Is there an easy way where you can perform a search of your own questions or apply a filter (Say I only want to list the questions that has a regex tag on it)?
Yes. Go to Advance Search. You will get more tips there.
user:me is:question [Regex]
user:me is better option if you want to search your own questions.
If you want to search other user's question you can use it with
user:UserId like this:
Here 1455529 is your
UserId. Put other user's
UserId to search their questions.
is:question limits the search to questions only.