During Harry Potter and the Deathly Hallows: Part 1 the crew (now reduced to only Harry and Hermione) wander through the Forest of Dean when a Patronus in the shape of a doe leads Harry to the frozen lake where he finds the Sword of Godric Gryffindor. Later during the events of Part 2 we (and Harry) take a look at the late Prof. Snape's memories and see that it was actually Snape who cast a doe Patronus (supposedly to Harry's aid), much to Dumbledore's surprise, who therefrom deduces a relation to Lily Potter (who Snape was secretly in love with all the years, albeit only unilaterally):
Dumbledore: Lily, after all this time?
Which already makes me wonder what Dumbledore was actually surprised about there. Was he simply surprised that Snape still loved Lily or was there anything deeper suggested with this Patronus? Add to this that Harry was a bit confused, too, and asked Dumbledore (or at least his mind-image of him, however you take that scene) about the reason for the related Patronuses, which didn't clear any confusions for me, though:
Harry: Professor, my mother's patronus was a doe, wasn't it? That's the same as professor Snape's. That's curious, don't you think?
Dumbledore: Actually, if I think about it, it doesn't seem curious at all.
So my first question would be, is there any deeper reason why Prof. Snape and Lily Potter both have a doe as Patronus or is it just to express that they've always been what one would call soulmates? And why did the Patronus appear in the Forest of Dean at that moment? Snape's discussion with Dumbledore and his casting of the Patronus occurred way earlier than that (as Dumbledore obviously was still alive, so at maximum during the events of the Half-Blood Prince). If that was implied to have been the same Patronus that appeared at the Forest of Dean (as the montage implies), why/how/where did it wait for so long? Is this just one of those various moments of stuff "magically" appearing when needed (as the Gryffindor Sword and the Room of Requirements use to do) or is there a more elaborate reason the movie just didn't delve into (or am I just too stupid to get it)?