In the EU, am I legally allowed to forward an email containing a conversation with my coworkers / bosses (no confidential information) to my private email address?
It depends on the content of the email and other things. You could be in violation of your work contract, it might be copyright infringement, it could be espionage, it could be totally harmless.
A simple test would be to ask your boss. If you would rather not ask your boss, then you might not want to send that email. If your boss says no, you might not want to send that email either.