Very subtle differences. Did is past simple, while have is called perfect tense. Both sentences are grammatically correct. Note that use of the past tense refers to a single, known occurrence, while use of the perfect tense refers to one of more occurrences at unknown or unspecified times in the past. I.e., I did go to New York. (a one time past occurence) vs I have been to NewYork. (a past occurrence that could be one or many times)

This is not a case of correct or not. Both are technically correct. What matters here is usage and you will very rarely hear 'why had you' now. It sounds quite old fashioned and formal.

why did you run away" is the correct term. and if you already use did which is the past form of do, using past form for the verb after is unnecessary.