How do I save the data from apps no longer supported by iOS 11?
You should be able to use iTunes to save all the data from these apps after the fact, but it's far better to export and save off data before you upgrade since you can't restore a device back to iOS 10 to run the apps or check on what data you need.

More specifically - once you are on iOS 11:


Connect your iPhone to your Mac or PC via USB cable
After a short while you'll see an icon appear that represents your iPhone - this should appear to the right of the drop-down menu (near top left of the iTunes window)
Click on the icon to view your iPhone's summary screen
In the left-hand pane of your iTunes window you'll see various options for your iPhone (e.g. Summary, Music, Movies, and so on)
Click on the File Sharing option (it should be the last one)
Now you'll see the File Sharing screen appear on the right-hand side of your iTunes window. This screen will list all apps that support file sharing.
Click on the app you want to save data from
On the right you'll now see a list of documents saved within this app on your iPhone


Now you can save the documents you want by selecting them and clicking on the Save to... button at bottom right.

NOTE: If you don't see the Save to... button at bottom right, scroll the window up so you can see it.