Merkmal, Eigenschaft and Charakter all seem to mean character.
I’ve seen Eigenschaft most often used in relation to science, for example perhaps in describing different types of stone, minerals and in the behaviour of animals. For example, if one were to say “the hippos exhibit aggressive territorial behaviours”, I would imagine Eigenschaft could be used in German, or maybe an even better example would be when one describes the properties of water and it’s behaviour according to different elemental states.
Charakter must be the closest of the three words in relation to the English character in the context of describing a person’s nature or behaviour. But that is just my assumption based on the similarity in spelling between the two words. For example: “His character is strong but he shows his softer side when he works with animals”.
A subquestion: Can Charakter also be used to describe animals?
Where would then Merkmal fit?