The battery percentage is only an estimate. Your phone doesn’t know the exact percentage of the battery, so when it restarts, it re-“guesses” the percentage, which may be different than the “guess” before it restarted. This may not be the case, or it could be a combination of this and a bad battery.
You probably have just lifted one layer of the screen off. If you see a big metal plate and the home button is still inside the phone, then you can use a suction cup or an iSclack to open the plate up. If this is the case, then your screen might be toast.