Question

It is said you cannot create apps automatically with the current facebook API.

Create and Configure Facebook Apps via API

How to programatically create a Facebook application via JS SDK or Open Graph API? (createApplication)

Yet woobox.com does it.
I have created a few photo contests in their portal. It didn’t ask for extra permission. No dialogs showed up. I just got these links:

http://www.facebook.com/pages/-/105892812908965?sk=app_422118604517529&app_data=dlt-1
http://www.facebook.com/pages/-/105892812908965?sk=app_451684954848385&app_data=dlt-1

How did they create these apps?

app_422118604517529
app_451684954848385

I would expect

http://www.facebook.com/pages/-/105892812908965?sk=app_SAME_APP_ID&app_data=WOOBOX_ID_1
http://www.facebook.com/pages/-/105892812908965?sk=app_SAME_APP_ID&app_data=WOOBOX_ID_2

Answer 1

You are correct with the presumptions that Facebook apps/users/groups and pages can’t be created dynamically. What woo box is what many other page tab applications are doing. They create a number of applications for different templates and then customize them according to your inputs. They don’t create apps dynamically. And these dynamic apps get their required data from app_data field.
Another point to note is

An app can’t be installed on a page twice

that is why many Service provider that provide page tab applications maintain a pool of applications to fulfill their user’s desires.