It doesn't show on update manager (as someone told it could be done thay way); Also, I updated kernel to .19 version but updater has new updates for .16 version... I have ppa installed, should I keep them? On updater settings, should all options be "ticked as ok"?
As stated in the announcement in the official blog:
If you’re already running Freya, you will already have received all of the above (with the exception of the newly added hardware support) in your regular updates.
So, by normally updating your system you get the 0.3.1 release (bar the hardware enablement stack). If you want the full experience, a clean install is always recommended.
I would recommend a re-install, using the 0.3.1 iso. You can do so without losing your data. See link
I would also do an Aptik Backup too. I've updated 3 systems to 0.3.1 using this with no data loss.