Why was Danny able to override his Cyberman programming? And why was the Brigadier able to, also?
"Because love, it's not an emotion. Love is a promise..."
Which is a call-out to John Lennon, “Love is a promise, love is a souvenir, once given never forgotten, never let it disappear.”
In that case, presumably the majority of people love somebody - why don't all the Cybermen overcome their programming?
In the immediate case - because the majority of the dead have been dead for decades, centuries,or millennia. The people they love are themselves dead.
In general... um, because they don't care about the plot hole this presents
Or, for the No Prize... because for it to kick in, the cyberman must 1) have incredible will (Danny, the Brigadier) and 2) be in close proximity to someone they loved before being made a cyberman. There is precedent for resisting Cyberman-assimilation in Matt Smith's episode "Nightmare in Silver".
Or, for another No-Prize: The process by which Missy made cyberman is different than other cybermen we've seen, so the statement doesn't generally hold at all.
If you have a TARDIS and your have a plane, is your optimal mobile headquarters the plane? Why wasn't his first order "Right, everyone into the TARDIS!"
1) Do you take the Master into a TARDIS? Really?
2) UNIT Protocols
3) As previously discussed (though, we disagree on the point) the TARDIS' ability to go exactly where the Doctor wants is unreliable. If he slips even hours ahead, to after the rain falls, he cannot go back and make it not fall without creating paradox.
Missy still had her disintegrator on her after being captured?
The tech with the glasses and bow tie had it on the desk, and was working on it. Missy gets free, comes up to the desk, and while the tech is distracted, Missy picks it up.
The Doctor was OK with her being left alone with a couple of guards despite knowing she's the friggin' Master?
Well, what else does he do? Keep watch personally, and thus get nothing else done? Will a *million* guards be sufficient? It is the Master, after all...