My German friend thinks that it is wrong to use "Did you ever" in the sentence "Did you ever fly a kite"? She is telling me it is wrong because you must use "Have" with "Ever", which would make the sentence "Have you ever flown a kite?". My argument is that "ever" is just an adverb, it shouldn't define whether "Did" or "Have" should be used. Is her argument correct?
The ever in questions such as Have you ever flown a kite? can be understood as in your life to this present moment. The present perfect (have/has + past participle) is used because in your life is conceived of as unfinished time.
It is the reason why the present perfect is used with other expressions that imply unfinished time:
Have you seen Mary today?
Has she finished the report yet?
Have they played golf since coming to Germany?
But if the speaker is referring to a period of finished time, then the simple past is used. So, for example, if you are just on your way to bed (and hence you conceive of today as finished time), then you would ask: Did you see Mary today?
The same applies to ever. If you are referring to a finished period of time (e.g. the childhood of a now adult), then you need to use the past simple:
(As a child) did you ever fly a kite?
So your German friend is wrong - possibly influenced by repeating an oversimplified 'rule' she learned in school, or by the fact that the present perfect in German is typically used with expressions of both finished and unfinished time.
Here is a similar example with je (ever) in German: Hast du als Kind je ein Haustier gehabt? = Did you ever have a pet as a child?
Your German friend is wrong.
Did you (ever) mail that letter?
This question, without 'ever', is a simple enquiry about a specific letter, in the past. Using 'ever' here suggests that the questionner thinks it at least possible that you never mailed the letter.
Have you mailed that letter?
This is very similar to the first version except that the questioner is allowing that there is still time for you to mail the letter (a 'yet' could easily be added at the end)
Have you ever mailed a letter?
This question asks whether, at least once in your life, you have mailed a letter.
Have you ever mailed that letter?
This is confusing (UK usage) - 'ever...that letter', a specific letter in the past, does not make sense with the unfinished continuous present perfect.