That phone was released in 2014, so I'm surprised it's usable at all today. I'm guessing you have one, but possibly two problems.
The short suggestion is upgrade the phone. It's too old to be worth fixing.
The long answer is it sounds like your battery is shot, which would explain the fast drain. Even with the best care, the battery won't last 5+ years. They haven't likely made a battery for that phone for nearly the same amount of time, so any "new" battery will be old stock and in about the same condition. Another possible issue, related to draining while trying to charge, could be something to due with the charging components slowing the charge current. A bad USB cable is often the culprit, but anything damaged between the wall outlet and the battery (so the charger, cable, phone port, or internal circuitry) is suspect until ruled out. A bad battery could cause this too, but rarely. You could try replacing the battery (if you can even find one) and see what happens, but I wouldn't hold my breath. If that and/or a new USB cable doesn't fix anything for you, it's simply going to cost more than it's worth to repair. You could buy a much newer phone with better specs, even if it's used, for what you'd pay to repair this one.