iOS5 split keyboard not playing well with some apps, including Apple ones
The new keyboard abilities in iOS 5 could cause quite a few problems for applications which haven't been updated to detect their use. In order to move content out from under the keyboard when it is shown, the application receives a notification whenever it is shown or hidden. However, if the keyboard isn't in the default position, the notification that it is about to be shown is not sent. Instead, there is a new notification which indicates that the keyboard is about to move. If you go back and forth between the default position and split/undocked, the application receives notifications that the keyboard moved, as well as notifications that it is shown and hidden. My guess is that Apple chose to have the status be "hidden" if the keyboard is not in the default position because it might not be necessary to move content in this case, but it doesn't make a lot of sense. 

What you are seeing with iMessages is that the keyboard is "hidden", so the app doesn't move its content. If your keyboard was undocked but not split, you wouldn't be able to read whatever was under it at all. Since it is split, the system adds a partially transparent box in the middle so that the entry field isn't floating on nothing, so the message is only mostly blocked.

The situation for Facebook is similar. It automatically hides the send button when the keyboard is hidden. Since the system doesn't send the "shown" notification if it is split, Facebook doesn't show the button if it's split either.

The only thing you can do is file a bug with Facebook and Apple. For Facebook, load the page for it in the App Store and click the "Send Feedback" button. For Apple, go to https://bugreport.apple.com/ (free developer account required). It is possible that Apple meant to send "shown" notifications for the split keyboard, in which case that is the real bug, but they should figure that out when they investigate the hidden messages.