I am in a situation, where I have to bulk-edit all URLs I have ever posted, preferably with a regular expression. Is that possible?
Natively via Facebook desktop, no, there is no way to do this.
Using iMacros or any extension based on the number of posts in the bulk can lead you to a rate limit block on your account.
Using the API via a third party application will not work either as third party applications cannot edit posts that did not come from that application.
So, the safest bet is to use the API with a Facebook native application user access token (i.e. a whitelisted Facebook mobile app), using the Facebook native app will ensure
- all posts are received
- lower the risks of rate limit occuring
- be able to edit any post
Within the scope of this site (since programming is off topic) all I can do is point you to references