no you don't need to constantly select for it. you only need to select for it once.
think of it as finding the coefficients to a million degree polynomial so that it passes through a million given points. each point is different -- the function, or weather, changes over time. but once you select the million coefficients that work, you never need to do it again.
yes in a total view of it, but to show the probabilities involved, you can't just find an initial state where it happens once, you need to find one that sustains it. this is of course ignoring the fact that you'd have to find an initial state where the air over blaland is not only still or constantly replenished with water vapor, it would require the global circulation to be stable in a way that it would not normally tend to, which would require either a lot of input energy or the perfect, perfect, perfect intial state. if it was still and only required an initial point, you'd have no way to make the water vapor rain. and you'd also have to figure out how the air would never move out of the blaland area faster than it is replenished. i wouldn't know how to prove it but i would lean towards the initial state is not possible, instead requiring a constant energy input in the right places, and this would affect other regions of the planet in ways that i would not know.
blaland's current climate would be dominated by dry climates, desert mostly, yes, but the southern parts are forest in the current position. the east is also grasslands. the only problem is the lakes region, which has enough lakes that plants would have moisture from the ground soil.
yes i'm not sure about the lakes their formation and stuff would be peculiar as would their sustenance but otherwise this is pretty accurate