The first thing here is from a CIQ app you don't have access to the actual .fit file that was recorded. You can record one, add things using FitContrib user data, but not read one.
And I can read it with a custom mobile app with Connect IQ Mobile SDK for upload later to a web server? If yes, I can register the mobile app for a message and when the recording finished I can send the message from the CYQ app to Mobile App and start sync.
No. Activites get synced by the FW completely outside CIQ. There's no way to trigger a companion app on the phone to do anything when an activity is saved.