An authority? You flatter me, anon!
The two most likely events for a death knight to regain their total free will were Acherus and the death of Arthas (and while there is no canon evidence of the latter happening, there is at least precedent, as the Lich King being severely weakened is what allowed the Forsaken to break free– I think an actual defeat would be more than enough to sever stronger-willed individuals).
As for now, we don’t know what Bolvar’s grip on his armies is like. His goal is to keep them in control, not actually conquer or destroy anything, so we don’t know how much slips through the cracks (or is allowed through). It’s possible that stronger-willed individuals are able to drift away from the hivemind, especially if they’re not particularly threatening (an ex-paladin who just wants to go home as opposed to some bloodthirsty maniac who devoted himself to the Scourge willingly, for example).
You could get creative with the circumstances, too! Perhaps the character in question… hell, I don’t know. Maybe they got stuck at the bottom of the sea for three years after their ziggurat crashed during the Northrend war and something something sea floor leylines something something Old Gods allowed them to break free. Or a lot of meditation. Who knows.
I’d not make up anything too convoluted because too much backstory, in my own experience, makes a character harder to develop (or be of interest to anybody) in current times. But you could easily contrive a way for a DK to break free after the events in Icecrown.
The second question is much easier!
Regular people lose limbs and manage without them all the time. I’m sure a magically-animated, superpowered, semi-immortal killing machine could get along just fine without an arm. A little inconvenient in some combat situations, perhaps, but nothing too impeding. They’d just have to adjust their fighting strategies and techniques accordingly, and hopefully they never end up in a situation where they have to maintain a handstand and are suddenly very itchy.
There’s also precedent for DKs mutilating themselves as a form of penance (Ormus the Penitent, the gear vendor in ICC, tore out his own eyes). While your question makes it sound like it was an accident that they view as some sort of cosmic payback, they are definitely capable of experiencing guilt over their actions and having a desire to repent.
Actually, we know a little bit of what Bolvar’s control over the scourge is like! There was a lore panel for what I believe was the Cataclysm reveal, and they said that the transition between Arthas and Bolvar’s reigns was not an easy one and that he lost control over all of the Scourge in the plaguelands.
It would not be too far of a stretch to say that during the sundering of Frostmourne, your character was in the plaguelands and between Arthas losing the Helm of Domination, Frostmourne being broken and Bolvar taking the reins as Lich King, your character was freed not only from the Lich King, but the entirety of the Scourge.
I am on mobile now, but I will get the exact quote when I get to a real computer.