I´d like to create a program which will react on actions by user in real time. For example there will be three Labels. And when user clicks on one, I want to recolor the border to a different color and the user should be able to "type" a (single) number in this Label. I know about the Entry widget, but Labels are suitable for the whole application. 
Thank you for any answers
Your question is too vague to answer precisely, but to specifically address each individual point:

Yes, it's possible to "react .. in real time" -- whenever an event is detected it will be acted upon as soon as possible.
Yes, it's possible to color the border of a widget when an event is detected
Yes, it's possible to type into a label. Though, obviously, the behavior is unusual and may not be what you expect. 

I suspect none of those help you solve your real problem, but I have no idea what you're actually trying to accomplish.
How to react on actions (events) in real time in Tkinter?