In your question, sentence 1) is the right construction.
Yes "Asked whether the discussion ..." = "When asked whether the discussion ..."
In the case of sentence 2) I would advice against using 'being', starting the sentence with 'being' is not wrong but it is lousy. 'Being' is used to denote a state. It can also be used to start a sentence when the sentence is in passive voice and the passive verb is the subject of the sentence, for example : being chased by a dog, he jumped over the high fence.
Sentence 2) does not necessarily mean that he was asked repetitively , please do not confuse the usage of the word 'being' as used to denote repetition. As I mentioned above 'being' denotes a state, like human being - (novice translation) human state , it does not imply any repetition.
About the difference between 3) and 4) , they are both correct, it is similar to the example I provided above, but removing 'Being' from sentence 4) does not make the slightest difference in the meaning. Again, please do not associate the meaning of 'Being' with 'A series of actions' or 'repetition' rather, 'Being' denotes a 'state' let me give you a few examples (pardon me if you could find the same examples elsewhere on the internet. No plagiarism intended) :-
- Being Indian,I have to get a visa for every country I decide to visit.
- Being Blind, I am happy I don't have to see the horrors of the world.
In all the above sentences 'being' indicates state, it does not mean a series of actions or repetition.
If I can make a conclusion about "one-off action versus a series of actions" in the first two examples
The conclusion you have to make is not about "one-off action vs series of action ", as long as it concerns the use of 'being' your conclusion should be about "Active and Passive voices".
I found a very interesting and similar discussion in this forum I am certain it will help you understand when not to use 'being'.