Do people tend to improve on thier 2nd and 3rd attempt?
Some do, if they made daft errors in their first, or were just immature. Good spelling helps.
If you total the amount of NATS and EUROCONTROL attempts, it totals 6, surely this must be enough to get through atleast one of them?
If you can't do it, you can't do it. This applies to about 95% of the population and that's what selection is designed to do. Select those who CAN.
What are the predicted NATS/EUROCONTROL recruitement demands for 12 months time?
For NATS, as many as we can get our grubby little paws on. If 2000 pass selection, we may have to delay the start of a few [well, most], but there is a global shortage of ATCOs at the moment.