Jiang, hello again. In my opinion, search for and search out are similar in meaning. You may say: the police search for the missing person and you could say the police search out the missing person. Certainly, the result of both actions will be the same.
Not so sure on your No. 3 at the moment, but for No. 2 I would prefer in both instances to use 'at' the edge of the water/cliff. To stand on the edge of the cliff would seem to suggest a very dangerous action and to stand on the edge of the water may get you wet.
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