Fair. The other example is, of course, the time heist. By stealing the infinity stones first, the Avengers should have prevented Thanos from getting his hands on them in this timeline and therefore from enacting the Snap that motivated the Avengers to attempt time travel. Instead, each heist splits off a new timeline.
Yes.
Each time they take a stone, they take it from another branch of the timeline tree, and bring it back into the original "trunk". They then return the stones, allowing the branches to return to the trunk. They very specifically (and explicitly - it was part of the discussion in the film) don't undo anything. They don't make the Snap never happen - they just resurrect everyone. There is no net meanignful change to the past.
Strange is trying to change his own trunk, make the death never have happened, without spawning a new branch, in a way that produces a paradox.
I suppose it's possible that Strange was deliberately trying to prevent the splitting-off of a new timeline, wanting to save his Christine rather than to merely create a variant of her that survived.
Exactly.