Hi Makoto,
Sorry it's taken me a while to see this post (work commitments and all that), anyway here's the deal...
The pushing movement that you described is prohibited within ITKF rules, although I tend to think that this is a good strategy to adopt to gain distance and surprise.
quote
7. PROHIBITED TECHNIQUES AND ACTIONS
7d grabbing, clinching, pushing or bodily crashing against the opponent.
As for the others,
7h Techniques which, by their nature, can not be controlled.
So the 'axe kick' is a definate no no.
Ura-ken is OK providing it meets the requirements eg target, stance, power, timing etc. the only problem with this though is the referee, and their interpretation of the 'effectiveness' of ura-ken.