I'm not sure of particles in these 3 sentences, especially this particle-の between noun/verb and ～方, are they OK? (If you see any other grammar mistake, you may let me know too.)
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～のVerb(pre-masu form) + 方 is the set form. ～をVerb + 方 would be wrong.
As you need to use the pre-masu form, 歩い方 would be wrong. 歩き方 would be correct.
何 implies a specific thing, like asking 'What is the thing that is the way of walking while wearing a kimono.'
It might be better to separate the two thus:
If you still want to place them in the same sentence, I would go with:
or, as @immateur has suggested:
If you were to provide the English of what you want to say it might be helpful.
I don't see anything wrong with this sentence. If you are asking about the purchasing from a machine, it would be better to say 飛行機の切符販売機の使い方を教えてください。
This is fine.