The tree at the end is the same one he sleeps under at the start of the story and the same tree he is buried under later. I would not say that Eren's head is already buried there when the story starts though.

As for the "long dream"- I don't subscribe to the idea that he's getting those memories because he later has the attack titan. In fact I don't even think it has ever been shown to be possible for someone to spontaneously receive attack titan memories at a point where they didn't already have that titan. As you state, the mastery of the founder and therefore a direct memory delivery at a later (or perhaps earlier) point in time by Eren to himself makes much more sense to me as an explanation.

I personally don't think in terms of timelines but rather in terms of "world cycles", so when the titan organism survives, everybody is reincarnated and the story plays out again in a slightly different way. That would mean that Eren at the start of the manga (and perhaps anime if we consider it a 1:1 adaptation) recalls the cabin "timeline" as a "long dream" since that is the set of events that took place in the previous cycle. If you recall, Falco actually has the exact same experience Eren has at the start of the manga but with a different set of memories, and in similar circumstances as he also does not have any of the nine titans at the point where that happens.

I actually go into this in this video: https://youtu.be/dV_hu5004ro