The alarm with snooze/view/stop appears in time. Once I click on stop button, it takes 5-10 seconds to stop the sound (as well as to disappear the alarm window). Until the alarm stops, I repeatedly press the stop button. The button press is probably not registered in first click (screen doesn't have any problem as per experience from other apps).

No it doesn't take 5-10 seconds for desktop to work after unlocking screen. Clicking icons works soon after. Although sometimes desktop icons doesn't works at all and I have to do killall -9 hildon-desktop to make it work. But that's a complete different story.