Share your experience!
When the screen is on the soft keys will not turn off, only when I watch a video. And my phone is vibrating now when I receive a message. Please help.
If you mean with "soft keys" the on screen home button and the others, they only disapear in full screen aplications like movie, photo or some apps and games.
The vibration when you receive a message can be turned off in the configuration of the phone or the app you're using.
But the used to cut off after a couple of seconds. Now they just stay on. But not when I watch a movie. They stay on during the home screen, app drawer, fb, anything that is not a movie
In my case the're also on the whole time, also in the most apps. Only while watching a movie, pictures or using the camera app they disapperar, and while playing temple run. I think this is depending on the app.
But it also might be connected with the new android version. 
But it drains my battery. And we all know xperia does not have a big battery like the galaxy's
The "on screen" buttons drain you battery? Are you sure you're talking about the Xperia Z?
The buttons wouldn't use more batterie because they're always there if your screen is switched on. They are no extra knops, they are "on screen". And only if you use an app that requires the full screen (like a movie) they will disapear to make room for the video. Else they will always be there like the task bar in windows.
I hope this would help.