Is Kozlov an Iron Fang?

A 'Bane Witch' is a 'Bane', same as 'Bane Knights', 'Bane Warriors' and 'Bane Riders' are all 'Banes'

It's likely omitted to prevent a rule interaction that they didn't want, probably No Sleeping on the Job since Knockdown immunity is a big deal for casters.

She also gets to run desecrator gunlines in Black Industries. Accumulator [bane] ftw.

Because different casters in different factions get different rules. Also as others have pointed out Kozlov had a spell for knockdown immunity.

Might be fluff rather than rules interactions. Especially as we can't see a rules interaction that doesn't already exist for a caster. Tacitician can be given to Maddox via the Storm Knight captain and Vet Leader to Rask via the Mist Speaker.

From a fluff perspective, according to the IKRPG core book: "Although the Iron Fang legions are a close-knit organization where most members would rather die than leave their brothers in arms, sometimes men do leave the legions for their own reasons. Those who do are seldom welcomed back."

Kozlov seems to have been an Iron Fang in the past, but warcaster training (and his own aristocratic obligations) might mean that he had to leave. Even though those are probably good reasons for leaving, that doesn't mean he would be welcomed back as a full member. Close-knit groups aren't always rational about people who put something other than the group first.

That was a whole kurfuffle near the end of MkII. Someone asked about Forgeguard with Murdoch getting Desperate Pace from Finn (I think it was DP, don't remember what Finn did in MkII) and were told that it only works on Murdoch. Somehow the thread got the attention of a PP staffer (I think it was Shick) who came in and basically said "Yea, if any model in the unit has a tag then that unit counts as an X unit, did you guys not know that?"

That set off a huge wave of people looking for these interactions and looking at specific instances of single-word tags inside multi-word tags (like, is Eiryss a "Mage" because she has the "Mage Hunter" tag?). They ended up doing a fair bit of errata around it and I think they pulled the unit bit in MkIII but AFAIK any individual word in a models name, type, or subtype lines can still be an identifier if they chose to use it. 

By your example though, it would only matter if there was a rule that effected "vampire models" in the vampire hunter model's faction. Most of the time it doesn't mean anything, but like others said it works for anything that's tagged as "Bane" for example.