Battery and heat issue

I need some early diagnostic of my iPhone. The battery drain really fast. Standby time is only around 8 hours, normal use is about 2 to 3 hours. It also tend to heat pretty high during usage. It also never showing battery usage info in battery menu in setting. I've tried to consult with some technician, he said my battery is worn out but I kinda feel it's something else because the symptoms were a bit different. I've also checked it with some battery health app, all of them shows my battery is still in perfect condition.

I've tried to recalibrate the battery several times but nothing changed. I even DFU restored the phone twice but it's just the same.

Notes: I bought this phone about a month ago from someone through an online marketplace (pre-owned). Previous owner said the battery have been replaced so it's not the original battery anymore, and my guess it's might be a cheap/fake one. He didn't even have the original charger anymore so most likely this iPhone have been charged with third-party charger which I don't know if it's certified or not. And since I'm the only iPhone user in my house, I have no choice but chare it with an Xperia charging port.