tenses - Is there any difference between the questions beginning with "have you ever" and "did you ever?"

I understand that the question beginning with "did you ever" is normally used to ask about a state or habit that doesn't lead up to the time of speaking.

for example:

Did you ever see her (while you were in London)?

The question beginning with "have you ever", by contrast, is used to mention a state or habit up to the point of speaking, so adverbials like 'in your life' would co-occur with the question.

However, I've also come across a lot of examples of "did you ever" in which a state of habit in question doesn't seem to belong to the finished past time, but to the present time.

Here are some of them:

• Did you ever hear of anything more silly?




• Did you ever think maybe you're not too big? (from the film, "Big
  Fish")




• Did you ever try cocaine?




• Did you ever hear of such a thing?

Each of the speaker doesn't seem to narrow his/her question down to a specific time in the past. Thus I suppose, while it is true that "Did you ever?" normally asks about things in the past, the question can sometimes mention things in the present time (rhetorically, sometimes). How well do you think it is supposed to be true?