Hey,
The edge (see image below) becomes bent when I use the chamber/filet tool and I don’t understand why. I guess it’s because of the cylinder with a cone on top but I don’t know how to solve/work around this. Any ideas or help is appreciated 
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That’s because the original surface is not flat. An edge is just the intersection of two surfaces. The chamfer’s surface is flat, the other surface is not, thus their intersection is also not flat.
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Thank you, does that mean I need to redo the whole thing properly? Right now it’s a mess.
You can just simply cut off the top part and redraw it.
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Welcome to the forum Hugofrost
As Istvan suggested, the simplest thing to do here is to cut the offending part off and then extrude the new flat face back out.
While you think its a mess right now, in reality its an easy fix and you will gain another bit of knowledge that will be useful later on.