If I stay on 7.1.2 firmware, should I backup My Apps to Itunes? I have an app installed on my device running iOS 7.1.2.
Say I delete the app.
In a few months I CANNOT download the app without updating to iOS 8.

If I "backup the app" using Sync onto Itunes, can I recover the app compatible with 7.1.2?
or will it still require me to have iOS 8?

Alternate Q: If restoring the app via Itunes sync fails, what Other methods can I save and recover the older version of the app?
Unfortunately by "backing up the app" it only backs up the data the app has. You can go into your finder and locate the app and save that in another location and when you need it inport it into iTunes. Just remember to not update the app.

Finder/username/music/itunes/itunes media/mobile applications