I prepare myself to be shot down in flames (as I am not a pilot in any way) but if from what I have gleaned from on here is correct then:-
1. What is de-icing paste exactly?
Anti - icing is the ability for the aircraft to take preventative measures against icing - i.e. using icing boots or bleed air from the engine to prevent ice from forming on the control surfaces. I would say from the name that anti-icing is performed when icing conditions are expected and may not be effective once icing is known.
De-Icing is where measures are taken to remove ice known to be present. Using again boots, bleed air or what ever is available. Once you know the ice is there you are trying to counter act it.
Gladly shot down in flames to learn a little more