You have to pick:

If this happened, would we, in this universe, even notice a difference?

We'd notice it almost immediately since suddenly there are all these new people wandering around in confusion at how they've been thrust into a parallel universe. :)

I think this would create a rather brutal economic shock. Some areas of the world will see famine and violence (mostly the poor third-world areas that are already on the edge), and even in prosperous first-world areas we'll suddenly have just half the capital resources per-capita that we did before. Having half the population suddenly be homeless and undocumented would be a huge challenge for our various governments. It'd be like everyone just absorbed a massive surge of refugees.

Ooooh. I thought it said "the new people are shunted TO a parallel universe" but it says they are "shunted FROM some parallel universe"

Does this only compress your height?
After 1000 sneezes you'll be 36.77% of your original height. You'd start becoming very oddly-shaped if it didn't shrink all your dimensions.
Do the WYR Pixies magically make it possible for your body to function at extremely small sizes?

Your body stays at the same proportions and yes, the WYR pixies make you able to survive at tiny sizes.