Can I use tabs offline?

Yes, tracks you opened when you were online are cached and will also work offline. You don't have to play the whole track to cache it for offline usage - just wait a few seconds while the whole track is being uploaded to your device. Half speed and solo tracks are downloaded from server as well, so you need to turn on half speed (or solo) and wait a few seconds if you want to use these features offline.

Each normal speed track is about 1Mb. Half speed tracks are about 2Mb each. Offline cache size is 500Mb by default. You can change the cache size in Settings - Songsterr.