New iPhone 15 heating and battery going down fast

Hello, I bought my brand new iPhone 15 three days ago and I’ve noticed some uncommon fenomenons. When I charge it it over heats ( I use the 20-80 rule and if it’s charging from 20 to 40 it’s already heated. Also I don’t use it meanwhile) and the battery goes does relatively fast despite it being a brand new phone. I went to sleep on a 77 percent and woke up to a 60 smth, also when I’m using it for texting and stuff it also goes down quite fast. I bought this for the 20 hour battery of video reproduction so if I’m not watching a video it should last more right? I’m going on a vacation that involves a road trip and a ferry (24h in total approx to reach my destination + more hours of road trip to my stay), I don’t want to constantly be worrying about my phone and plugging and unplugging it and if it overheats while doing so. I already called apple support and they said everything is fine w my phone.

Is this normal? What should I do? Has this happened to anyone during their first uses of their phone.

btw I also haven’t done a backup transfer so everything is new and I also disabled some of the setting that drain battery like the background app refresh and so on.

Please help