Duhg has the following:

A MOTLEY ARMY FROM ALL NINE REALMS: When building your force, if Duhg is the highest-point character, other characters that share a keyword with him also have the Duhg's Army keyword.

So, how does this work? Does it mean that "If, when building your force, Duhg is the highest-point character, then from now on, all other characters that share a keyword with him also have the Duhg's Army keyword"? If so, that would mean that opposing characters might get this keyword too.

Or does it mean "If Duhg is the highest point figure when you build your force, then other characters that share a keyword with him (but only while building your force) also have the Duhg's Army keyword (for the rest of the game)"?

And how does this interact with replacement characters? If Iron Viking was a part of my force when building my force and got the DA keyword, what happens when Iron Viking is replaced by Iron Pharaoh (who does share a keyword with Duhg)? Can we say that the gaining of a keyword was a game effect that transfers to the Pharaoh? Or do we say that it doesn't matter because anybody with a shared keyword will gain the DA keyword as long as Duhg was the highest point figure way back when I built my force? (This could matter if a non DA character is replaced by a character who could qualify for the keyword.) Or is it too late for this new character to get the DA keyword?

This line from the PG might apply:
Game effects that are applied to a character prior to replacement are applied to the new character accordingly. If the replacement results in multiple new characters, then the game effects are distributed as decided by the characters‘ controller.

It would transfer the same way as an ATA, relic, resource, etc. They would need to share a keyword still.

Not 100% though.

I don't know about the replacements part, as I haven't kept up to date on all rulings concerning them, but since it doesn't specific friendly, it would work on opposing characters as well.

Nice for those with keyword-based targeting. Good catch.

It only applies when building your force, so there are no opposing characters yet. They do not gain the keyword, because they are revealed after the force is built.

I'm not sure if the sideline counts as part of your force for this effect, so I can't speak to that.

D'oh. I focused on the one part, and forgot the other.

Good catch.

When assembling your force, you identify these replacement characters although they are not yet on your force.

That said, a replacement will retain all game effects from the previous character. In this case they will still be under the effects of the traits, but will still need the shared Keyword in order to gain Duhg's Army keyword. If they are replaced again and regain the shared keyword they will also gain the trained one again.

Oh, also, if Duhg is KO-ed, do the keywords he gave people stay or go away?

From the Core Rulebook:

Game effects remain a part of the game only as long as the character continues to possess the power or ability. If a power or ability is countered or lost, all game effects of that power or ability immediately end, but any actions already in progress are resolved normally.

This is one of my biggest problems with the Heroclix core rules. This paragraph should NOT apply to a figure being KO'd. Is there anywhere that says when a character is KO'd they lose all powers and abilities? It just says remove them from the game. There should be a separate section for what happens when a character is KO'd.

And this isn't a new pet peeve. This has bothered me all the way back to GSX with Sabertooth. He was kinda the first figure that had a power that went around being countered or lost. There was no precedent, so they ruled if he was KO'd it kept going. Then it just folded the two things in ever since. KO'd is the same as being countered or lost. It feels like a sloppy shortcut and not a well written game rule.

This is something that is under discussion. We are looking into characters that were written under rules that had Durations and how they should work under current rules.