Thank you for asking! Answers are for this post and I'm still taking asks if anyone else is interested! I've already answered one for Kaiba and would be happy to talk about my other faves. :)
I am going to call him Duke in this post if you don't mind. I'm dub trash and that's his name to me.
1. What Pokemon would you compare this character to? (may be replaced with "what Digimon" or other such monsters / critters if needed)
Ooof, this one was actually really hard! Duke is a pretty complex dude to me, and since there are no dice pokemon, there's no easy answer. The best source of inspiration would be his manga arc to see his core development, where his father was training him up to replace someone else and steal his destiny. As far as symbolism/themes surrounding him, we've got clowns, dice, ninjas, and revenge. I cannot for the life of me think of a single pokemon that really embodies who he is, either in terms of absolute pure canon OR the fleshed-out personality I've interpreted him into.
But what I can do is give you a pokemon team for him that captures some of the story and visual themes surrounding him: Greninja, Porygon, Mime Jr., Gimighoul, Yamask, Pawniard.
Greninja, Gimighoul, and Pawniard are included for the monsters he uses in DM and DDM. Mime Jr because he's literally the son of a clown and embraces a tiny bit of that aesthetic for himself. Porygon because he's a bit dicey-looking and his origins are pretty technical and scientific, something that I associate with Duke based on all the work that went into him creating DDM. Yamask because when he did approach Yugi and the gang at first (they approached him actually, but I digress), it was under false pretenses. Charm and deception are two sides of the same mask and this boy wears them both way too comfortably.
7. What might they appreciate as a gift from someone?
My answer for Kaiba on this one was long, so buckle in! With Kaiba's, I basically went through the different kinds of gifts that would be good for him and who would give them, so I'll do the same here, based off of the different ships/friendships I imagine for him.
Generally though, I think what Duke values in gifts is either the thought and effort that were put in (handmade stuff, or something basic but deeply meaningful) or the kind of gift that is activity-oriented (bro loves hanging out with his friends).
Ryou has a good few options. He's an artist and Duke has always been really supportive of that. He might make Duke some custom resin dice based on his Monster World characters, or custom resin dice earrings based on his Monster World characters. I think the best gift he would give Duke is a piece of art starring all their Monster World characters from the campaigns that Ryou runs, and the whole thing is set up like a fun movie posted. Duke would be so thrilled with it. He'd get that framed and insured and hang it where he'd get to show it off. In the end, it would be some work of art that integrates their shared interests/activities, which makes it especially personal.
Ishizu would, I think, give Duke a modern copy of the Ancient Egyptian game sennet, or maybe a different game that she might have grown up with. He enjoys a challenge and trying new things, and he would also appreciate that it's something personal from her life that she's trying to share with him. Plus, more games are more things to do with friends.
I think all of that could apply to Marik as well. I also think that Marik, as stylish as he is, might have a pretty good grasp on Duke's style and get him some accessories and new nail polish or makeup, stuff like that. (You can't tell me Duke doesn't wear makeup, just look at that eyeliner!)
Kaiba probably fumbles the first time he tries to give Duke a gift. Either it comes across as patronizing or too aggressive, or just somewhat off. Duke decides to take the time to explain that what he wants most from Kaiba is dedicated time with him, so planned vacation it is. Seto says he can take him anywhere in the world, and Duke doesn't care where they go, as long as he is the center of Kaiba's attention.
Hm, time for Joey. Now, here's the thing, I've got a few pretty different Joey's running around in my head, all at different levels of maturity, so bear with me. He might want to take him out to do something special or have dinner at a really nice restaurant—an experience instead of an object, and it's time spent together. When in doubt, or just as a backup, Joey will have some special intimacy planned as well, and that's consistent for whoever Joey is with.
12. What's a moment in canon regarding them that you feel is underappreciated?
Hnnnnnngg I just made a big long post recently with all my Duke Devlin propaganda, because honestly, I think most people do just see him as a pretty face, that guy who flirts with Serenity to piss off Tristan, and the guy who put Joey in a dog suit, and that's it, but he's so much more than that to me. I'll cover some little scenes here that I either think about a lot or that I think are generally forgotten until you go back and rewatch the show.
One moment I think about a lot is that two frames of him making stirfry in Season Four.
I don't think you'd believe how much of my understanding of Duke derives from that moment? I think about it way too much. He stepped up to cook for his friends, he handles that frying pan with confidence, and from that I think I extrapolated a lot of my more domestic/mundane headcanons for him (like how he always makes sure his partner/s are well-fed and looking after themselves, and that he's generally a pretty responsible guy, keeps his affairs in order, all that jazz).
Another great moment is in the KC Grand Prix Arc when Joey and Tristan step in front of a TV camera and are making fools of themselves and Duke just steps between them and the camera, showing his good side and smirking. I don't think he even says anything, and it's great. It's just a casual "the camera loves me, and you idiots need to stop making yourselves look ridiculous." (Couldn't find a screenshot or gif of this moment, sadly.)
I think the first time we see him in the anime is this scene where he's in an office or apartment above his game store and is just watching Yugi pass by (with unnamed sycophant next to him). It's an almost creepy moment, honestly, and it's the kind of thing that makes me toy with the idea of a full-villain version of Duke.
As far as the manga goes, I haven't read most of it (I got the first few volumes shortly before my recent move, and they're packed up somewhere still), but I know the gist of his manga arc. Yugioh is full of bad dads, and I think because his dad got cut out of the anime it's easy to forget that Duke's a member of the Domino Bad Dad Support Group as well.
Anyways, I hope that's a satisfactory answer. I feel like that was pretty long-winded heh. 😅 Thanks again for asking! I do love talking about my boy Duke.