Is it possible to predict how busy an airport will be in a given time? (are there existing services that to this?) I want to know if it's possible to predict how busy an airport will be at a given day or part of day.

I know there are services that provide the scheduled flights in an airport


Is there also an API that allows programmatically accessing this data (preferably for free)
How far in advance are the flights scheduled and the data published? 


The distribution between 'regular' passengers and 'connecting' passengers is also important (a passenger during a connection has a much lower effect) - it the data of how many passengers in a flight taking a connection available? (even long term statistics)
This is a bit of a different approach than you were thinking, but Google estimates how relatively busy a place is based on location data:



This can be found in the right-side bar if you search for an airport code or many other locations. It's based on their location data, not flight schedules.