Charging port problem or something else?

My Inspiron 5565 battery will only hold a charge for about 1 hour so because of that I have it plugged in all the time. When my laptop is getting low it never tells but instead decides to shutoff with any notifications which is frustrating. I had changed out my battery last year because that battery was essentially doing the same thing.

The problem I am having that is of most concern is the charging port. I recently purchased a new charger because I was having problems with charging my laptop. I would have to move it into a certain position so that it charges or else it just won't charge. When it was charging the piece that is plugged into the charging port would get extremely hot sometimes to the point where if I were to touch it I could get burned. My new charger doesn't have that problem as bad but I still have to move the charging cord in a certain position so that it charges.

My problem can't be the battery itself because I had replaced that battery last year. Could the problem be the charging port itself or is there another problem I missed? Do I need to replace the charging port altogether? I never replaced one before so I'm still new to this. Also, my laptop does get pretty hot and my fan is constantly on so why is it always hot? I don't game or do anything big on my laptop.