As per my understanding, every time someone is traveling through time a new timeline is created. This fits with Bruce Banner explaining that you cannot change your past and the Ancient One which mentions alternative timelines. Unfortunately the Ancient One didn't say exactly if they just need the stone back or will continue with exactly the same timeline, therefore not everybody did agree on that.

Joe Russo explained: "You can't change the future by simply going back to past. But it's possible to create a different alternate future. It's not butterfly effect. Every decision you made in the past could potentially create a new timeline."

Wouldn't that mean that the events of the film Infinity War never happened, giving birth to a new timeline where everyone is still alive?

Yes

There is a timeline in which Thanos disappears before the Infinity War, so that the Infinity War never happens in that timeline, but it is never shown nor mentioned after Thanos left. Captain America later goes there to return the Power Stone.

Wouldn't that mean that the events of the film Infinity War never happened?

No

The point here is that the Snap happened as did everything after that in the intervening 5 years including the destruction of the Infinity Stones by Thanos and his death at Thor's hands.

The Avengers pull the Infinity Stones from various past times by means of travelling through the Quantum Realm to make their own Infinity Gauntlet and undo the Snap (at least bring back everyone who was snapped).

The Unsnap would bring everyone back to the point where it happens, i.e. 5 years later.

But

(newish independent timeline / loop)

Thanos in 2014 discovers the plan and travels forwards to 2023 in an attempt to stop the Avenger's plan. However, due to our heroes efforts he is defeated and Past Thanos is dusted.

Steve Rogers then returns the Stones (off-screen) to the points in time they were taken from thus restoring the original timeline where the snap happened.

This closes the loop and destroys only the timeline/split where Thanos came forward in time.

Certainly, there are some lingering issues regarding how Past Gamora in now still in 2023 and probably a couple of others but that's the main gist.

I feel a little sheepish doing this. But a good night's rest gave me some clarity on the situation and I wanted to share it.

The answer is in the timelines that are created because of time-travel.

If a person kills their past self shouldn’t they cease to exist? Well yes, only if both the present and past self are from the same timeline. When the team traveled to the past to get the stones, that very act of going back creates a new timeline.

In the original 2012, there was only one set of Avengers. In this new timeline, there are two.

The same applies to Nebula too, in the original 2014, there was only one Nebula, Quill took the Orb. The time travel leads to an altered timeline where Rhodes exits with the Orb. It’s the Nebula and Thanos (and party) from this new 2014 timeline that have come to 2023. Therefore Nebula killing her younger self will not affect her because the two of them belong to different timelines.

And finally ... the same applies to Thanos. The 2014 Thanos we see in this movie is from a different timeline, his death will not affect 2023 which has been through the Infinity War.

In short, all the past selves are from a timeline that is different from the main storyline we have seen so far in the Marvel Cinematic Universe.

I believe that it is supposed to be the same to return the Stones, as to return Thanos to their original point where they were taken in the past. Otherwise as stated in the movie, another timeline would be created.

However, it also stipulates that if you change the past, your future would not change but the other timeline future will be different.

Therefore there are now two timelines: the original from the movies and another where there was no snap due to Thanos vanishing in 2014.

One of the critical unanswered questions is

What does "dusting" really mean?

Clearly there's a distinction between "death"-by-dust and death-by-other-means. The gauntlet was able to bring back the Snap victims, but was not able to bring back Black Widow, Vision, Quicksilver, or anyone else who had died. (they certainly had time to try, since both the Pym portals and the van were destroyed in the fight, and they had to build a new one; and they had motivation too. Hulk was known to be able to handle a snap; Thor probably could; and maybe even Scarlet Witch - and she certainly had motive to try.)

I suspect that "dusting" actually sent the dusted people into some alternate place or dimension; into limbo; from which the gauntlet could also return them.

And in the case of 2014 Thanos at the 2023 fight, I consider it likely that dusting simply sent him back to 2014 (with his army) to where they belonged, possibly with a memory wipe or "reset". Or not.

So Thanos might notice a "what was that?" sensation. Or he might have suddenly, in 2014, gained complete foreknowledge of the 2023 fight, and that foreknowledge is what motivated him to do what he actually did between 2014-2018. It may even be the "spark" that made him say "Fine. I'll do it myself."

Of course it still happens. If it hadn't the whole movie wouldn't exist! Everything makes sense if you look at it from the way they explained it from the movie.

Going back into the past and changing things creates new timelines... sometimes. The rest of the times, it doesn't. That's because it already happened that way.

Captain America didn't change anything by going to the past and being with his love interest because it always happened that way. That's why when he ages he is in the same timeline. For the most part they didn't change anything when they went back into the past. It always happened that way - that's why they had to replace the Stones so that the Infinity War could happen.

The only new timeline created was Thanos when he discovered Nebula in the past. That comes to an end when the Stones are replaced. It's not that it was destroyed - it did happen after all. People remember killing him in the future. Stark did sacrifice himself. All of it happened, it's just that the original timeline was restored and the side timeline is merely disconnected.