Just a note on the bolded: Pretty sure the entire sequence of codewords has to be said in order
In order to trigger him completely - yes, I agree, the entire sequence is needed.
However, I'm pretty sure that he begins to get triggered from the very first word. One-two words is enough to make him listen at least, otherwise he could have put his fingers in his ears, shouted 'LALALALA' and that's it. Zemo wouldn't have been able to trigger him. Especially with his horrifying Russian accent.
Not to mention that he went into cryo because he was afraid someone would trigger him again. You wouldn't do that if you are a supersoldier and the only way to make you listen is to restrain all of your body.
Also, I think Hydra made sure to have a reserved emergency way to get him back in case he breaks the programming and gain back some memory.
The order was to kill Bucky. They weren't there to arrest him, it was to kill him, so the escape. He doesn't trust anyone, I think even Steve.
This entire scene bothers me. Like, yes, they have the order to shoot on sight. However, it's obvious that they have this order only because everyone knows how dangerous the Winter Soldier is. Would they have shot him if Cap apprehended him already? Like, it's Cap! Everyone knows he's a good guy and fights against terrorists.
Also, why War Machine didn't do the job? Why instead the task force was sent to risk their lives?
Steve told Nat that he would bring him in. But he haven't done any actual attempt to do so.
Also, keep in mind, that they had this cage with them. So I don't think that the order was to kill in all the cases.
As for the Bucky being on the run. I understand his reasoning, I understand he doesn't trust anyone. And I don't actually blame him for it, but he definitely should have come to Steve. At least to Steve as soon as he got his memories back. He knows someone can use him again, he admits he knew it all this time. But this is exactly the reason why he should have come to Steve. Society will always perceive a person on the run as a criminal. If he is on the run, then he is still a Hydra's terrorist, not brainwashed Captain America friend.