All three sentences are technically correct -- except for the phrase 'asked to his parents', which I will explain further down.
Yes, there is potential ambiguity in the first. This would be resolved in a full discourse -- in the surrounding text, it could be made clear that the protagonist is still living, or that he outlived his parents for some time. The ambiguity could be resolved in the other direction within the sentence, confirming that they all died at the same time, by having 'Those were the last questions he asked his parents before they all died.'
The second is unambiguous, but stylistically awkward. In English there is a great dislike of repeating the same words within a sentence when there is any alternative -- this is why pronouns are so useful. We could resolve the ambiguity within the sentence if we knew the names of the parents, in which case we could have 'Those were the last questions he asked his parents before Henry and Beatrice died.' -- but then we would need to know (from the rest of the text) that his parents were indeed named Henry and Beatrice.
The third is fine, as it is obvious that the protagonist -- I or me -- is still alive (unless this is a story being told by a ghost!), or the story would not be being told.
As for 'asked to his parents', the verb 'ask' is a simple transitive verb, taking a direct object ('his parents'), not a prepositional phrase with 'to' indicating recipient ('to his parents'). Although, on further thinking, this would work: 'Those were the last questions he asked of his parents before they died.'
The following sentence, however, would be fine: 'Those were the last questions he put to his parents before they died.'