BAKURA'S MILLENNIUM RING
Marik: Silence, fool! I would run you down with my obligatory anime motorcycle, but I just noticed you have a Millennium Item. What is the deal with that?
Bakura: Oh, my Millennium Ring. Yes, that's mine. I use it to manipulate the fabric of time and space, bending it to my will in order to create shambling monstrosities that feed on the souls of the living. And sometimes I just use it to find gay people.
Marik: Why would you wanna do that?
Bakura: Secretly, I'm very lonely.
--Episode 33, "Harpoonshipping"
So...yes. Aside from technically being where his spirit resides, Bakura's Millennium Ring helps him put pieces of his soul into other objects; to make spirits of trading cards manifest in the real world; to shoot Ancient Egyptian Laser Beams at other Millennium Items; and to do pretty much anything the plot dictates he needs to do, including always regaining his Ring no matter how far away from him you throw it. Also it tends to glow and point towards gay people. Given his canon, this happens a lot.
MARIK'S MILLENNIUM ROD
Bakura: I have an idea, Marik. Why don’t you just use your Millennium Rod to take control of Yugi's mind? Then, he can just defeat himself.
Marik: You fool! Don't you know that my Millennium Rod is powerless against Yugi? It only works on people called "Steve". Why do you think all the Rare Hunters have the same name?
Bakura: Wait a minute; if that's true, then why did it work on Bandit Keith?
Marik: Well, duh! His middle name is Steve! Just check his Wikipedia page if you don't believe me.
Bakura: Oh... well that's a rather annoying limitation.
Marik: Look, I don't make the rules. The rod only works on guys called "Steve"... and girls called "Steve"... but believe me, those are really hard to find.
--"Marik's Evil Council of Doom 2"
Primarily, Marik uses his Millennium Rod to pose suggestively to control his henchmen's minds and make them do his evil bidding. He can, however, only control people named Steve, and "his evil bidding" usually means "playing a children's card game". Somewhat like Bakura, Marik can leave pieces of his soul about thanks to the Rod, but his depositories tend to be people - those he's possessed, for the most part, though Abridged-canon makes this a bit fuzzy due to the Rod working...differently than in usual Yugioh. Once Marik has left a piece of his soul in someone, he can take over their body even when not in possession of the Rod, and can also communicate with them telepathically. (As I doubt Marik'll find many Steves, all this likely means is that Marik and Bakura may converse in thoughtspeak now and then.) The Millennium Rod also has a knife blade concealed within its handle, which his evil(er) alter ego Melvin enjoys quite a lot. (Why sometimes it's a knife and sometimes it's a Sith lightsaber may never be discovered.) Finally, Marik once exploded an underling's head with his Millennium Rod, but this seems to have been a one-time occurrence.
POWERS SHARED BY BOTH
Melvin: Perhaps we should settle things a little more traditionally: with a children's card game. But not just any children's card game - a Shadow children's card game! Ah-hahahaha!
Bakura: God! Is that really how I used to talk back in Season One? I must have sounded like a total wanker!
Marik: Yes, you did, you sounded exactly like a wanker.
Bakura: I was being rhetorical, Marik.
Marik: A rhetorical wanker!
--Episode 46, "Melvin'd"
All Millennium Items can be used to send any game the wielder is playing into the "Shadow Realm", where the loser must be trapped forever and all damage is real. While playing a Shadow Game, the wielder of the Item responsible can also create supernatural penalties during and after the game - for example, when dueling against Marik's darker half Melvin in the season 2 finale, Bakura's body disappeared gradually as he lost Life Points because Melvin decided as much (having been the one to announce the Shadow Game). (Bakura's Ring can also apparently take duels to Silent Hill. Go figure.)
Both the Millennium Rod and the Millennium Ring have been shown to emit painful "yellow squiggly lines" of energy that propel people backwards/freeze them in place. The Rod may well be every bit as capable of firing Ancient Egyptian Laser Beams as the Ring, but if it's done so the instance escapes me and thus Marik won't be lasering anyone. (The lasers only seem to activate around other Ancient Egyptian magic, anyway.)
Though this ability is unrelated to their Millennium Items, both Bakura and Marik possess the ability to break the fourth wall - they're pop-culture savvy and are aware of their existence as characters in a TV show - characters who must fight with the protagonist for as much screentime as they can get. If they know your character's canon as a TV show -- and ironically they're more likely to identify a western-canon character than an anime character, since the creator of their series isn't actually an otaku -- they won't be shocked that a TV character is real, but they will likely break the fourth wall to offer opinions about the show in question, etc.
Finally, though this isn't technically a "power", both Marik and Bakura have alter egos. Marik has a pure-evil "darker half" named Melvin (created out of years of physical abuse and live-action Disney movies), whereas Bakura possesses the body of a mild-mannered, very British and completely forgettable boy also called Bakura. It's highly unlikely that either of these two personalities will surface, but pushing Marik to the brink of his sanity will bring Melvin out and taking the Millennium Ring off of Bakura will release his host. Anyone who puts the Ring on will in turn be possessed by Bakura.
In a nutshell, I need to know:
Is your character gay? Is it OK if Bakura's Ring reacts to him?
If your character happens to be named Steve, may Marik take control of his mind?
May Marik and Bakura break the fourth wall around your character?
Advice for your characters, should they wish to avoid danger:
For the love of Ra, don't play games with these guys.
Keep your hands off of the Millennium Items.
Bakura is not a kitty. Handle with care.
Thanks muchly! <3 Have fun with a couple of men obsessed with their fancy jewelry.