Svetlana was the one that 'suggested' Las go to Kazakhstan.
We know Sveta is both strongly precognitive and excellent at reading probability lines. She also knows much of what happened at the Assol complex. It's entirely possible she foresaw Anton would need a lift and persuaded Las to get the right train, knowing he would get off at the same spot after the spell wore off.
As for why she went to the trouble of calling him, that allows her to cast a weaker (and thus less detectable) spell while also deflecting suspicion away from herself.
Olga has swapped bodies with men quite often already.
This is a Wild Mass Guess for the Day Watch movie, and it is quite a small one. But based on the way Olga was preparing herself to be strangled from behind and the fact that she is already comfortable with passing for Anton among his colleagues, it seems like Olga must have done this before. It makes sense, since she has been a Night Watch agent for a long time, working under Geser and being a pretty close friend of his, that she was his go-to person for mind-swapping a person as a decoy.
- Not to mention knowing the way around the wrong voice. And she was remarkably comfortable with him feeling his/her breasts/ass/groin. Then she let him go off with his girlfriend, knowing he was almost certain to let her in on the secret.
Merlin's riddle wasn't a warning.
Colossal spoilers for The Twilight Watch follow.
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Merlin's riddle says "Proceed if you are as strong as I. Or turn back, if you are as wise as I." Anton takes this to mean that a wise Other will turn back, as the seventh layer of the Twilight is incredibly dangerous.
However, by working with Nadya, he is able to break through the barrier at the bottom of the sixth layer, and gets to the first layer, because the layers are cyclic, with the surface world being both the zeroth and seventh layer. While it takes a lot of power to get there from the sixth layer, he could have gotten there easily simply by going back up through the layers of the Twilight.
And that's what Merlin's riddle actually meant. From the sixth level, one can reach the seventh in two ways. The strong other will use brute force to open a portal, while the wise one will take the easier path of going up to the zeroth level, which is also the seventh.
- What is this doing at WMG page? This one was spelled almost leter-to-later in book itself.