Ok but do I understand correctly that when I want to acquire Bitcoin with fiat via Bisq that Bisq only handles the Bitcoin transfer while I have to use the traditional banking system to wire the fiat money?
You can transfer the fiat using any of the usual electronic methods or via cash.
Once financial authorities get involved asking me for the origin of my coins
How do they know you have any coins? If you've done things properly, then you've traded exclusively peer to peer, you've not signed up to any centralized exchange or other centralized service, and you've not handed your KYC over to any third parties.