Battery drain, overheating with a perfect new battery

I have some complicated issues with the battery in my IPhone 5s. I have it since 2 years and recently the battery was getting worse and worse, I also observed overheating at the back, bottom side. Yesterday my phone died and I was charging it for 8 hours - the only result was that it was stuck on the charging animation and it wouldn’t turn on (It seemed like the port was detecting the charger but it did not charge my phone). So i went to a service and just to check, I plugged in an original charger (recently I was using some non original cheap ones) AND it worked! BUT I was adviced to change the battery and so I did. Now on the battery life app it shows the battery is in a perfect condition but in fact it’s being drained even faster. It goes from 100% to 0% in an hour. What’s funny: I have two chargers (NONE of them is original) and while one is working Ok, the other doesn’t charge my phone at all. What could be a problem? I read something about U2 IC damage but in these cases either the original charger did not work or the phone could not be charged with any charger - which is not the case in my phone. Could you please give me any hint about what could be wrong and how much would I pay to repair it? Thanks!