Why would a Government agency risk burning a zero day if they can just pay that lady or blackmail her with something else?
Hacking implies a sophisticated attack.
Not saying either government didn't do it. Following paxys line of thought I would however agree that hacking is not the most likely explanation in how the private data was taken.
Social engineering is sometimes also described as an "hack" but I doubt that is what Bezos implies with the word.
Depends on the audience I guess. The big majority of hacks are not sophisticated at all. There's also so many people that use it without an implication on the grade of sophistication.
But one thing is true, we can't possibly know for certain his intentions by using that word :-) so these are just our opinions for now :-)
to you and me, yes. probably also to Jeff Bezos. but to the general public (arguably the real audience here), hacking is anything between guessing someones weak password and sophisticated attacks like stuxnet.
As an example: consider the FBI pushing Apple to help them decrypt a terrorists phone from several years ago. They finally got in because the phone was a particularly old model without a secure enclave and (from memory) they ended up buying a 0day for a considerable sum to do it.