Is there any program that will schedule events on the iPad such as activating airplane mode at a certain time and switching it off after a certain time, or closing all programs?

Not unless you jail break. The iPad's operating system, iOS retains a very tight control over what programs can and cannot do. It limits the interaction that programs can have and what control - if any - they can have over the operating environment. So it is not possible for one app to close or open another, nor for apps to interact - except in a very limited sense and that is very strictly controlled by iOS. Although this imposes certain limitations - such as not allowing the sort of functionality that you're proposing here - it does have many advantages, not least of which is that the iPad cannot get a virus.

Tim

There might be possibility to do so if Apple provides such feature in their public SDK. To find out you need to look into iOS docs. However probability to find one is probably low.