Yes, as the sibling post says, it's effectively the same in most cameras and it's exactly the same in certain cameras (not many). Unless you, of course, actively fuck up by shooting a very low-exposure (dark) shot with low ISO (then you lose precision, because your analog measurements get quantified into small integers, that are also close to the noise floor), or by shooting a very bright shot with high ISO (where your highlights get multiplied right out of the range of your output format). If you don't actively try and fuck up the shot (AND you shoot RAW), you can make pretty wild changes in post and the data will be there.

That's just one more reason not to be afraid of auto ISO. The camera will choose something sane and you'll have ample room on both sides to get the image you wanted.

If you have an ISO-invariant camera, then yes - the final image would look the same whether you shot at low ISO and raised it in post versus shooting at a high ISO and doing no further editing. You can try it yourself. Or you can read the numerous reviewers who have already done that in the past decade, such as DPReview.