Appearance should be 現象, 跡象, or 表面？ This dictionary page lists many options for appearance: http://www.cantonese.sheik.co.uk/scripts/wordsearch.php?level=0

現象, 跡象, and 表面 all seem like good candidates.

1) Which one is the most common one to use when translating appearance in Mandarin?

2) Which one is the best for Cantonese?

3) Which one is the best for Don't judge things by their appearance? 看事情不要看現象? This one seems common, but doesn't 現象 translate more into phenomenon? Wouldn't 看事情不要看表面 be better?
There’s a common idiom that expresses not judging people by their appearances:

人不可貌相

Oxford defines this as:


  don't judge by appearances


and gives the full phrase as its example sentence:


  人不可貌相, 海水不可斗量。
  As the sea cannot be measured with a bushel, so people cannot be judged by their appearances.


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The sentence you gave: 看事情不要看表面 is a good sentence and it concisely expresses what you want to say. 现象 can also mean appearance, for example ABC gives the sample sentence:


  光凭现象做判断
  guāng píng xiànxiàng zuò pànduàn
  judge according to appearance only


but phenomenon is still the most common usage.

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Another word you might want to know is: 长相, which explicitly refers to one’s physical appearance, looks and features.