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1.  Using "keep" is to state a condition.  This condition can use
     "clean",  "cleaned" or "cleaning" to describe.  However, 3 of 
     them mean differently from each other:

  keep his house clean: 保持他的房子清潔
  keep his house cleaned: 保持他的房子被清潔
  keep his house cleaning: 保持他的房子正在清潔中

2. you can use "being burn", but the correct one shall be "being
    burnt" or "being burned".  Since you smell when it is burning, 
    so you use "burning".

3. No, using "overcooked" is not "past or present perfect tense" (
   過去 or 現在完成).  It is just "passive voice", means "被煮過頭" 

4. If economy can be grown, then I guess every president in this
    world will hire you to be their Minister of Finance.  Hence,
    economy will take its own path to grow, we just contribute to its 
    growth, we can control it in some degree, but not in a total control.
    Hence, you shall use "fast growing".   However, in some situation, 
    you can use "fast-grown", for example: 
   
    Google is a fast-grown company in the world.  
    Electronics device is a fast-grown technology.