After the takeoff, still during the climb, the engine started to make a louder and somewhat metallic noise that lasted for maybe ten minutes, like if it was struggling to work on full power.
It was probably the red diesel that they sometimes run on. Makes strange noises, that.
Is it a completely normal thing that one can hear when sitting next to the window on the wing?
No, usually you can hear chavs chanting "Maga Maga Maga-luf!"
Or is it that the engine was actually having problems?
No. Don't worry.
Can the pilot hear these noises from the cabin?
Sometimes. If Olga, Johanka or Magdalena aren't yapping.
Seriously, you are worrying over nothing.