It does NOT remove files from the DVR under most circumstances. There are a few exceptions to that regarding DRM.
You CAN tell how much battery and how much storage is left on the HopperGO using the settings menu on the DishAnywhere app.
@sjshowal56 - I mentioned in the review that you can see the storage and battery life remaining in the Dish Anywhere app. What I meant in the Bottom Line is that you can't see how much juice is left by looking at the HopperGO itself.