Hi ogox,
We are still looking into the sign in issue, but as far as offline mode:
If you have an engine installed completely, you should be able to launch it from offline mode. Make sure to check the library tab to see if you can launch the downloaded engine from there.
Another possibility is that the engine was in the process of downloading/updating when you last exited the launcher. If this was the case, you will have to wait until you can sign in to complete the download.
Try and follow TJ’s instructions on how to get debug logs while attempting to sign in if the troubleshooting guide does not help you. This will help us out greatly in solving the issue.