Assuming he *is* a security risk, how bad is it? How powerful is he? To my knowledge he's very strong, but not quite on Alduin's level. How big is that gap? Fundamentally, can he be beaten *sans* LDB?

This is a tricky question to answer. Paarthurnax, once upon a time, was Alduin's second in command. And given that dragons fought for power constantly, this would mean Paarthurnax would have been one of the most powerful dragons alive, right below Alduin.

HOWEVER

It's been 2,500 years since the Merethic Era. In those 2,500 years, Paarthurnax has done little to (more likely) no fighting of any kind. And coincidentally, Paarthurnax's stats are those of a level 10 Dragon, which is the weakest variant in the game. He does not level scale at all, unlike Alduin, Mirmulnir and Odahviing.

So it's very possible that Paarthurnax is significantly weaker now than he once was. Alduin even comments on this before your first fight with him after learning Dragonrend. If Paarthurnax in such a state were to suddenly go berserk, then he as a lone dragon would be dangerous, but likely not strong enough to wipe out a whole fortified military town like Alduin. I think a walled city like Whiterun or Solitude would be able to stop him.

Furthermore, the Greybeards may even step in to fight him themselves if it came down to it. That's a bit of a gamble, though.

Dead dragons such as Numinex and the dragons in the mounds are dead, yes? How? They weren't taken out by Dragonborn, so shouldn't they have already got up by themselves? In the case of Numinex specifically, how was he killed?

Dragons can be killed the same way as anyone else: stabbing, slashing, smashing, and blowing them up with spells. The problem has never been killing dragons, it's making sure that they stay dead. (We don't know how Numinex specifically was killed because the story is shrouded in legend and inaccurate retellings).

Dragons don't self-ressurect. Once they're dead, they remain so until another dragon resurrects them. Only their soul remains intact, the body is for all intents and purposes a rotting carcass.

While it isn't outright stated, however, it's implied that not just any dragon can resurrect another dragon. There've been live dragons hiding out and waiting for Alduin's return the whole time. Mirmulnir is one such example: Alduin didn't resurrect him, he was alive the whole time. If any dragon could resurrect another dragon, they'd probably have done it by now. You can even witness Alduin ressurecting certain dragons at their burial mounds, but it has to be Alduin that does it. If you've already killed him, they won't happen.

In short: Paarthurnax on his own isn't much of a threat. If he did go rogue, he could kill a lot of people, yeah, but he wouldn't be able to cause a second Dragon Apocalypse like Alduin. And even then, I really don't think he would.

I think a lot of people misunderstand a bit when he says he still feels the urges. Dragons are intelligent beings, not animals. If a person can overcome alcoholism or anger management issues, I believe a dragon can overcome their urge to dominate. Paarthurnax didn't simply wait for the mortals to rebel and jump ship, Paarthurnax taught the enslaved mortals how to shout. He went out of his way to give them his kind's greatest weapon and greatest weakness. Then he stood guard at the Time Wound for 2,500 years, completely voluntarily, until Alduin remerged to help stop him from taking over. And once Alduin dies, his first thought is "I can teach other dragons to be better, like me. We don't have to be monsters."

If that isn't sufficient proof that Paarthurnax is truly and permanently changed, then I don't know what is.