Even to this day, I have heard of many variations/interpretations of a "Cut Kick", so I will choose not to answer question #2 just yet. Could someone offer clarification and/or recommend a link to a picture of the kick in action?
On the other hand, I believe "Push Kicks" are open to less interpretation. If the part of the foot below the ankle bone (permitted technique) is delivered accurately and powerfully to the legal scoring areas of the body, then it should count as a valid point. I believe the only exception to a Push Kick not counting as a valid point is when the leg is not retracted immediately and remains on the hogu for a brief period of time. A possible case is when the extended leg is used to push the opponent back for a period of time, instead of with a quick blast. Similarly, a push with the closed fist is legal, as long as one does not straighten their arms and keep the push going for several seconds.
Hope this gets some discussion rolling for another good case of "You Make the Call".
Since the USAT site is down for the moment, you can still access the WTF Competition Rules at http://www.wtf.org/site/rules/competition.htm. I think the areas we need have little to no difference in this country unlike, for example, uniform of the contestant.
A quote from Article 12.2 about valid points:
Points shall be awarded when permitted techniques are delivered accurately and powerfully to the legal scoring areas of the body.
If a kick, say a push kick for example, uses a permitted technique to a legal scoring area, the only hair left to split is whether or not the kick fits the meaning of "powerfully". From the above Article 12.2, Explanation #3 states:
Sufficient power is demonstrated as the opponent's body is abruptly displaced by the impact of the strike.
And so we continue on the path of splitting one more hair: Did the kick in question abruptly displace the opponent's body by the impact of the strike? If the push kick is used in a manner where the extension of the leg after the foot is placed on the body displaces the opponent, then it is not sufficient power for a valid point. However, if the kick abruptly displaces the opponent by the impact alone, then it must be counted as a point.
Looking forward to some more input on this matter.