Give this a read to learn a litel more about how iCloud works: http://www.apple.com/support/icloud/
Not every app will show up in Notifications (just those that have notifications as part of thier functionality), nor will all show up in icloud (only those capable of storing content in icloud, for example).
As for the crashing issue ...
Try a rest: Simultaneously hold down the Home and On buttons until the iPad shuts down. Ignore the off slider if it appears. Once shut down is complete, turn the iPad back on using the On button. In some cases it also helps to double click the Home button and close all apps from the tray before doing the reset.
You may also want to take a look at useage (Setings app > General > Usage) and see how much free space is left. If you are running much under 1GB of free space, consider deleting some content.