I don't think Blood -- or any Aspect, really -- has any significant innate powers over peoples minds. The notion of the Aspect everyone associates with bonds, camraderie and direct leadership having the supranatural ability to basically flip peoples perceptions of one another on their head doesn't vibe with me. Even with NPCs who are supposed to be easily effected by Aspect powers.

A Witch/Prince of Blood sounds more likely to me to accidentally manipulate relationships around them through how they act, rather than as a knowing act at first. Although some of the more malicious or clever sorts may go for this with intent too -- but not through Aspect powers, rather through the social savvy those Aspects represent of their personalities in their cases. They also wouldn't necessarily be competent/successful at it, unless they learn overtime like with any other skill or are just really naturally good at it. No charisma roll bonuses, just a tendency to try rolling charisma in the first place.

I also don't think being a Blood hero inherently gives you a psychic awareness of peoples relationships/bonds and what to do with them. Some may not give you an awareness at all and you may just blunder your way into, out of, and through relationships with varied degrees of success. Like Karkat! He managed to keep people together as a team, but never quite 'fixed' their relationships or realised their potential in full, with some of them ending up going catastrophically wrong in A5A2. It leaves you to wonder how some of those super God-Tier full doomed timelines went, and why...

Seers (and maybe Mages? It's been a while) are near certainly an exception to this given their overall role, being able to see the possible best of people and their connections with others around them but even they don't get a clean and easy 'heres what all that means' or 'heres what to do to fix/ruin this' guide with their awareness. Thats something they need to figure out themselves with the information given, like any Seer. They could always be dead wrong, but they could also know you and your entire species potential -- no, destiny, better than you know yourself. It all depends on them.

That aside, I'd think Bloods active abilities are probably not anything to do with a specific element like Earth or -- god forbid -- literal Blood/bondsbending, but rather channelled into Objects of Association.

Weapons, outfits and any other tools people are bonded with -- their personal possessions. Like giving a sword a Red Buster-esque homing projectile as a ranged attack, change an items form to an equivalent at will without need for an alchemiter or being able to recall a lost item, or even teleport to it -- like a teleport-dagger, or something. Really making the most out of things, even if my lame examples don't quite sell it. (I really like Kevins point about Blood having an association with 'potential', by the by.)

Or, hell, what about a Ring being channelled with an attack that is eventually inescapable and never loses sight of its targets, and augmenting itself with the powers of new Sprites. I think the Prototype Ring could plausibly be a Blood-bound weapon, given it's most common wielders and exact functions. I don't think theres even much of a conflict of interest with the Rings of Life and Void having those powers too -- Blood working with and augmenting other Aspects seems to be in its nature.

And Blood has power with people too, of course. Buffs to people working in lockstep with one another for the strongest combos, letting people share unspoken battlefield awareness with one another for inhumanly good coordination, and maybe even stuff like outright combat heals/revives in a pinch (like somehow causing your friend to reanimate as a Vampire-type), or borrowing others powers, Aspect or otherwise, at a really high, God-Tier level.

But thats all on Blood from me. I'm fairly sure other people said most of that already in their own less rambly ways than me. As for other two:

I think Doom and its abilities focus around inevitability, misfortune/least fortunate paths and managed decay/curses. Things going for the worse. They could cancel out a Light players RNG manipulation, or hit a random bystander with the worst luck for a day like a petty asshole. No specific element or force at play besides entropy and chance.

Close a probability field and make all their enemies guns jam or their pets die and computers explode or just hit them directly with a debilitating status effect like blindness or starvation if they're feeling particularly unsubtle -- this whole curses thing Sollux was even doing without any Doom powers! Just plain reality editing codescripts built on closed loops that seem to be common on Alternia, but nobody else is actually any good at.

As for Rage. Rage...

I don't think Rage gives you the power to see through illusions, or glimpse 'the truth', or never be manipulated ever. Rage isn't objective truth, its just enabling someones distain towards percieved falsehoods, or things that are only false from a certain angle in favour of things that are only true from a certain angle. False superiority. False theology. False love. BLASPHEMY.

It's telling that a Rage player went on to become a straight up theocratic double-dictator within his empire of residence. A religion of murder-torture-at-will built entirely on a misinterpretation of two devil figures, even if the devil figures were in fact real and it did in fact guide exactly one of them to greater standing, at the cost of being stuffed in a fridge, thrown through a black hole, beaten with a crowbar and shot to near death on a regular basis for a while. What a deal, am I right?

I believe it is only fitting their powers are focused entirely on augmenting the self. Enabling feats of great physical destruction, endurance, projected stature, narrative derailment and other rulebreaks (e.g breaking the medium/timeline to sneak into a session way ahead of everyone else and cause havoc, Jokerkind specibus wielding any weapons), psychological domination (augmented chucklevoodoos) and intimidation. The assertion over all that would stand in or against their way, physically and psychologically, while refusing to be put down in kind. Depending on the class, they could share this with others -- build up a horde of angry, disillusioned sorts to throw at whoever they see fit like attack dogs. Which sounds kind of like an origin behind the clown cult on Alternia, really.

And despite how all that Rage stuff sounds and how it's been shown by the Makaras, Hiveswap and Friendsim both show some less incredibly fucking dangerous Rage representatives. People who could or even certainly would use it for good -- to uplift an idea besides just murdering people who are 'lesser' than you to appease your sacred Clowngods. To undermine ACTUAL falsehoods. It'd be interesting to see what those people could do with the Aspect if they were properly Classpected. No Classpect is innately good or evil, Rage just got a very bad hand in Homestuck with people who straight up are.

...Wow, there was probably a more concise way to say all that. Hope it's interesting.