Mostly just names, although since they’re self-chosen names that often relate to their early operations, you’d be right to assume that sort of thing is how the Underminers started out. As for the Tectonic Knights, they’re a chfssssc legion, so they specialize in fighting down-deep, the chfssssc natively dwelling down around the Moho.
Don’t take the name too literally. They’re a dedicated special operations legion, old - originally a pre-Imperial unit from High Daëntry - and very, very good at what they do.
Well, there’s a couple of things to note, here.
First is that the best way to deal with a hostile weakly godlike intelligence is to catch it before it blooms (hits hard take-off). They started our handling hostile emergent intelligences on a much smaller scale.
But the other thing is that the thing about gods? Sometimes gods are dumb and/or crazy.
Okay, so that could use some explanation.
Fully flowered seed AIs are instrumentally smart. When it comes to figuring out means to achieve their goals, they’re very, very good at that. But in the field of ends, it isn’t necessarily so. An entity like the Transcend is the ideal here, because it was made to serve some very broad purposes in the first place, and soaked up tremendous breadth of mind from all of its constitutionals. Something like that doesn’t have mental weak spots to attack.
But look at some of the others we’ve seen in canon:
The Leviathan Consciousness is very instrumentally smart, but its focus is incredibly limited. It’s obsessed with network process optimization and can’t see the world in terms of anything else. Civilization is largely protected from it because if it’s not connected to it over a networking protocol, it’s irrelevant, therefore invisible.
Or the Mistake, formerly the Eteolis Mindweave, which was intended to share some of the properties of the Transcend, but due to lacking the high-order coordination functions ended up tearing its own mind apart in the throes of a cosmic-scale schizotypal disorder.
They could go forth and poke either one of those, for example, without Transcendent backup, because their irrationality opens up big mental blind spots you can sneak up on them and punch them in.
Not necessarily vehicles, but the largest and most dangerous entities in the battlespace, yes. If the standard loadout can’t handle it (which takes a lot of work, since the heavy infantry are routinely issued pocket nukes), these guys go in.
Their on-person loadout is standard (after all, it’s all general-purpose equipment), but their doctrine includes extra training on specialized defensive equipment: dropwalls, rapid-deployment bunkers, SAFEs, minefields, etc., etc.
No, they’re just a normal special operations unit. The name comes from an old saying that “the one hope of the doomed is not to hope for safety”, something which reflects a lot of the missions they end up being send on.
Oh, yes.
(Well, a lot of the time they’re more like bear dragoons, but still.)
In the modern day, yes. Of course, back when the Ancyrans first invented the notion, it was more “And now, my son, you must go into the mountains as I once did, find and tame your bear, and ride him TO GLORY!”)
(Of course, at the same time, on Paltraeth, the kaeth were fielding ankylosaur cavalry armed with giant hand-held black-powder cannon[1], so it’s not like they were alone on Team Beyond The Impossible[2].)
They specialize more in the delivery of messages than the follow-up…
Not really.
And not within itself, but there’s always an occupation zone somewhere that needs policing a little more, um, vigorously than the Watch Marshalcy provides for.
Yes, actually, really big and thick ones based on heavy vehicular armor and requiring considerable power-assistance to lift. It makes them very slow, but also completely relentless when it comes to advancing under fire. Brutally hard to grind down.
Not routinely. (The 153rd is an exception because the transfer between services at their own request.) The Home Guard are defensive militia units, whereas the Legions are regular military, and you can’t just go around changing the terms of the enlistment like that.
(Well, okay, some governments would, be the Empire is institutionally committed to Not Being That Guy.)
The 32nd are an experimental technology legion, so their job is field-testing equipment and doctrine as regular legionaries; while the 141st is a special scientific legion whose name is literally accurate - the complex battlespaces of the future, especially at the edge of the known, sometimes require fielding people who are both trained legionaries and trained scientists.
Actually, you caught me in a mistake there where I described the same function in two different ways. They’re both artillerists/bombardment specialists, using weapons accompanying them into the field - artillery battery robots, mostly, these days.
(Orbital bombardment is left to the Navy to provide.)
That’s exactly what they’re intended to do: on stellar husbandry arrays, in coronal habitats, and other similar facilities like that. (As for the details of their weapons and doctrine, that’s something I’m going to save for future writings.)
Possibly. Of course, they’re also not using the same timeline everyone else is using, so it’s also entirely possible that their equipment is standard issue in whatever part of the future they originated in. It’s also possible that these amount to the same thing. Either way, preserving causal integrity means they aren’t telling anyone. 
Oops. You caught another mistake of mine there. The 161st should be listed among the light cavalry legions, as an aerial-operations unit. (In light cavalry terms, this means their personal vehicles are capable of functioning as “attack helicopters” or operating at multiple levels of three-dimensional battlespaces.)
If they have the recipe, sure.
But if some new, interesting, and potentially useful exotic material shows up out there in the hands of hostile forces, you’re going to need to retrieve a whole lot of it from them for analysis so that you can figure out how it works and thus how to synthesize your own version.
As a winnowing legion, they’re tasked to deal with guerilla warfare and insurgencies in occupied regions, primarily in urban terrain but occasionally elsewhere (based on thoughts and sources here). They sort out the wheat from the chaff, protecting surrendering civilians and escorting them to safety while eliminating all hostile forces in a designated area.
No, actually. As strange as it can seem to say about a military service so thoroughly trained and equipped, the Legions are the arm of restraint. If they’re on the field at all, it’s because the Warmain in command doesn’t want to kill everyone.
(Even specialized terror legions like the 56th and 98th are the arm of restraint, in that their function is to terrify, intimidate, and deter, and you can’t do that unless you leave people alive to be terrified, intimidated, and deterred.)
In the extremely rare case that the mission objective is “Wipe them out. All of them.”, an Admiral on a starship in orbit gives the nod, a gunnery officer presses the “Saturation Bombardment” button, and it’s all done and glassed by teatime.
Like the Roman genius or the kami, the legionary patron spirits are embodiments of the collective “soul” of the legion, its honor, courage, and other qualities. They keep (and are) its history and its lore, and they inspire and guide its legionaries, who may connect with them to seek such.
Not as such. The eikones represent unique concepts in Flamic theology, and between them the Noble Warlord and the Laughing Warrior encompass all that is uniquely war.
Which is not to say that other eikones have no place in warfare; Barrascán patronizes all guardians and protectors, among whom are many legionaries; Dírasąn likewise all messengers and couriers; Éadínah nand Leiríah smile on all who lay cunning plans and deceptive feints; and so forth. And, of course, every legionary who’s ever found himself under fire or pinned in a foxhole offers a prayer to Athnéël.
But they aren’t gods of war. Merely gods in war.