Intriguing observations. They are all very similar, yes. If you want to get into what the nuances of their distinctions might be, here are my thoughts / examples:
He is a man given to wine. She is given to her beloved.
The word I think of when I hear that a person is "given to" something, is "dedication". It can of course be the good sort (given to a betrothed) or the bad (the bottle). Regardless, their fate is intertwined with whomever or whatever they are given to. They will be seen spending much of their free time with this subject.
My mother is a woman marked by compassion. The merchant was marked by greed.
"Marked by" is interesting because it is very visual and implies that there is something so prevalent about a person that this quality is almost (if not literally) visible. In the literal sense you could have a dog marked by a scar. In the symbolic sense though, which is what you're more interested in I think, you have a characteristic so visible that it could even make itself known as you observe the person from a distance.
The potassium tea is characterized by a distinct banana-like smell.
This final phrase is one that in my experience is usually describing a positive or neutral trait. I have rarely come across descriptions of things "characterized by" negative things or evil. I suppose this could be the result of the old adage "It's good for you, it builds character." If something or someone is characterized by a trait, they are easily classified by that thing. To me, it is the least dramatic of the three phrases.
Final thoughts: In all three phrases, this thing that they are marked by, given to, or characterized by is a core, inseparable part of who they are. This is usually in a way that to attempt to separate them from this quality would be traumatic like trying to tear off a limb. They would lose a part of themselves, who they really are, were this to happen.