Do we know, canonically, how long ago Bathier ran away from home? I can't remember if the game tells us. But I agree, given how young he is, it can't have been *that* long, and he must have been able to make a pretty good guess that "Lamont" was Larsa Solidor. And I'm pretty sure the recognition was mutual -- although Larsa has to have been small when Balthier left, there is a family resemblance, and Larsa is pretty sharp.

In that conversation with the Order in Lowtown, Basch calls Rehks "the perfect witness", which pretty much confirms that Vayne was using Rehks to pin the murder on Basch, which he couldn't have done if he'd died in Nalbina. Unless perhaps Vossler found Rehks there, and he lived just long enough to blurt out his story. But I really think Rehks has to have lived long enough to make it back to Rabinastre; otherwise the white room scene makes no sense at all.