Hi all!
It’s hard to describe my observations tonight.
I press Space button to play, but it starts recording. And it happens only if Cursor stays at Left locator position. I stop it and press Space again - all ok. Then place cursor to Left locator and press Space - it starts recording.
Transport → Common Record Modes → Start Recording at Project Cursor Position is selected.
I close 9th version and open 8th version to check if something globally changed. Nope. Then I saved empty project from v.8 and open it in v9. All is ok. Maybe it is small thing, but I wont be happy if it happens at record session with many people waiting while I fight for freedom! 
Maybe I should use the 8th version, which is more stable than 9th?
It’s like Windows - one version is stable, next one isn’t, next - stable… and so on. WinXP ok, WinVista not, Win7 ok, Win8 not, Win10 ok (I hope).