Pressing the spacebar to preview is convenient in AE CC2015, but, why does audio start after 3 seconds, even when all video is cached (green bar)?
I am not able to preview my complete compositions, only after they are played once, the second time (in loop mode) will play all correctly.
Does anyone have a solution? Or is it just a bug?
Yes it's a bug...2015 is infested with bugs. Apparently they are taking AE apart & rebuilding it from the ground up...unfortunately they released it before it was put back together.
To fix your problem go back to an earlier iteration, 2014 or before.
Here are instructions on how to get older versions: http://blogs.adobe.com/adobecare/2015/06/16/how-to-find-and-install-previous-version-of-ad obe-apps-in-cc-2015/
There is meant to be an update coming out "at the end of the month" that fixes a lot of bugs. Work in CC 2014 in the meantime and then, when the update comes out, give it a try.
(But make sure you don't let the Creative Cloud app remove your old versions as it defaults to do: keeping previous versions installed when installing CC 2015 applications )
If the update doesn't fix the bug in CC 2015, please file a bug report: Feature Request/Bug Report Form