Here's a statement from Russo Brothers themselves.
Q: [Endgame’s] plot, is it a parallel universe or a closed time loop?
A: Nope, not a time loop. Both Ancient One and Hulk were right. 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. For example, the old Cap at the end movie, he lived his
married life in a different universe from the main one. He had to make
another jump back to the main universe at the end to give the shield
Let's address that Back To The Future confusion first. As to why they say it's all bullsh*t and then do something very similar to what Marty and Doc did - sneaking in the backdrop of a prequel.
In BTTF, when you go back in time, you don't create a parallel alternate timeline. If you goof up, you replace the original timeline with the alternate version. When Biff changes the past, the future is re-written, the original timeline has been erased leaving only the new, alternate timeline. So they go back in to the past to fix stuff. Once they do, they once again re-write the timeline with a corrected version. At any given moment only one timeline exists. And this gives rise to the Grandfather Paradox.
In the Endgame, traveling back to the past means going back and creating an alternate timeline which lives along side the original timeline. The original timeline is not re-written with the alternate version. Removing stones is one way to create an alternate timeline. But there are other ways to create them.
Every decision you made in the past could potentially create a new
For example, the two Nebula's interfering creates a new timeline, this is well before they go near the Power Stone. 2014-Thanos gets to know the future (that 2023-Nebula is from) and this creates an alternate timeline. Even if Steve returned the Power Stone, that wouldn't be enough to make this timeline vanish.
Now to the questions.
(Let's call the Original Timeline T0, and 2014-Thanos is from Timeline T1)
Thanos is not there at all from 2014 because he went in a time machine and never returned, and another time line where:
The Original Timeline, T0, has already had Infinity War, 2014-Thanos leaves T1 and reaches T0 in 2023 where he's killed. In the end, if Steve returned the Power Stone to T1, that timeline will have an alternate future without Thanos. Perhaps Ronan will get his hands on the stones, we don't know, and it is out of the scope of this film (just like Loki who disappears with the Tesseract).
Thanos traveled to 2023 from 2014 and met the Avengers and lost. Ironman died in this timeline. Infinity war can't happen here.
2014-Thanos traveled from T1 to T0 and to the year 2023. T0 has already seen an Infinity War. T1 might see an infinity war, but it's not caused by Thanos because he's killed in T0. Iron man of T0 is dead, we don't know the fate of Iron Man in T1.
And the original timeline where Thanos didn't time travel in 2014, infinity war happened, people died, Thanos got beheaded, Avengers retrieved stones, and hulk snapped fingers to bring back the vanished ones.
Original Timeline is T0, where the snap happened in 2018 and was undone in 2023. After that, a 2014-Thanos shows up from T1 and is killed of, thereby not interfering with T0's past. Iron Man, Gamora, Vision, Black Widow and everyone who was killed for reasons other than the "snap", remain dead.