Certain apps are designed to run on the latest iOS enabled iPod Touch, and they just will not work on the older iPods because they cannot run iOS due to the firmware architecture, and it can't be upgraded, so, in answer to your last question, Yes, to a certain extent, eventually very few new apps will be backward compatible with all iPod Touch versions.
As for the battery issue, 2 days isn't bad still, depending on how much you use it. If I play games on my 4th gen it dies in a few hours, because the high res graphics eat the battery.