Knight vs pawn

Is there a trick to see if the knight can block or capture an advancing pawn? Or do I have to calculate?

(I am hoping for a trick like king vs pawn: draw a square from the pawn to the last rank and see if the king can enter that square. If it can the pawn can't promote).

You have to calculate. There are small rules but only in very specific cases, and the kings will play a role at some point anyway.  If the king can support the pawn and the other king is too far away this endgame can become very tricky. There is the Philidor square manoeuver (a lone knight can draw against a far advanced pawn+supporting king if well-placed) always useful to know, but some early situations are quite complex :

 White to play draws, but the play is very difficult and moves are unique and counter-intuitive (Grigoriev, 1938)

Hm, so calculating is the thing :-(

I find myself with my left hand index finger one part of my screen and with my recht hand indexfinger making silly movements on the other part of the screen... . Wife and kids wonder if I'm allright.

Am I allowed to touch the board in OTB if I make sure not to touch te pieces :-).

If I remember correctly it used to be explicitly forbidden by FIDE rules to touch specific squares to ease up analysis. I can't find it in the current rules but it's still bad practice, don't do it.