Russian were ordered to Kill Martha if Superman appears, not Batman. Because Luthor is so sure with the outcome, it's whether Supes bring Bats head or his mom died, and never even considered that Bats will have a change of heart seeing "how ripe his hate" toward Superman and bend on destroying him. Not to mention, The one hour rule that he made for Supes to bring Bats head to the Scout ship where Lex are ready there and will show the world how dirty this "false god" can be, hence that dialogue: "All the cameras are on your ship (scout ship), to see the holy...etc".
And finally he can killed Superman with his own creation made by his blood (where in his hubris, Lex thinks he can handle DD).
That makes perfect sense.
Beast froze because Batman showed up, not Superman. He did not know what to do because Luthor only mentioned the guy in the red cape.
When the one in the black cape showed up, they were confused, because there were no orders regarding him...
That is ridiculous.
Firstly, if we accept the premise that these mercenaries are prepared to die to kill Martha (because what else do you think will happen if Superman does show up and they kill his mother in front of him? Snyder has gone to great lengths to show this Superman is not a hero. He ignores crime. He kills. Why wouldn't he kill them?), why would they just freeze or hesitate when Batman shows up?
They aren't robot drones who've been programmed to only react if Superman shows up in their scanners.
Unless they are stupid to the point of ******ed, if
anyone shows up to save Martha, she's dead.
If the argument is "because he's not Superman", how does KGBeast know it's not Superman?
All he knows is that there are sounds of gunfire, explosions, breaking wood and breaking men.
He can't see what's happening in the next room.
If we accept the fact the he does know it's Batman, why didn't he set him on when he burst through the wall straight away?
If he wants to escape, setting Martha alight would be a pretty good distraction.
If the answer is the timer, what happens when it runs out and Batman's still around?
If it is a potential suicide mission, where they are prepared to die at the hands of Superman rather than let him save Martha, why try and back Batman off by threatening Martha instead of just killing her?
If it's not a suicide mission, why didn't he just set Martha on fire and escape as soon as there was a sign of trouble? The timer again?
Lex isn't running a game show where Superman can win his mother back if he beats the buzzer. He clearly has no intention of letting her live.
Which brings me to the Batman didn't kill the 'Beast defense of Snyder:
"So, I tried to do it by proxy. Shoot the car they’re in, the car blows up or the grenade would go off in the guy’s hand, or when he shoots the tank and the guy pretty much lights the tank [himself]. I perceive it as him not killing directly, but if the bad guy’s are associated with a thing that happens to blow up, he would say that that’s not really my problem."
Except 'Beast didn't light the tank. Batman did. They explicitly show the tank get shot in close-up, gas start streaming out and then ignite by itself.
KGBeast doesn't pull the trigger causing the explosion.
When his tank starts shooting fire from the bullet hole, Batman leaps over Martha and it explodes. He set it off like a bomb.
It doesn't take any real effort to address these plot holes, simply asking "why wouldn't Superman save her" and building the idea around that.
Instead, this creative team starts with the idea - "I want to fit 2 TDKR scenes in somewhere. Let's have Batman rescue Superman's mother and do it there, it will help establish the beginning of their relationship and trust", without even contemplating the absurdity of a man distrustful of humanity in general, philosophically opposed to Batman's existence in particular, trusting him to rescue his Mother, after almost being beaten to death and stabbed by him moments earlier.
You need a compelling reason for him to be forced into that position. Then, when Batman succeeds, preferably without killing anybody, then he might start to re-assess his position on the Bat.
Snyder doesn't even think of these questions that immediately come from the set-up.
Here's a very simple scenario that makes it more plausible for why Batman goes instead of Superman, and also removes the preposterous suicide mission element implied by the set-up:
Luthor didn't give Batman all the Kryptonite.
Martha has an exploding collar around her neck, full of Kryptonite. Lex has provided proximity sensors, keyed to super-dense biological material around the warehouse that are linked to the collar.
The collar itself has one, that makes it impossible for Superman to get within 3 feet of her without setting it off.
The mercenaries also have Kryptonite bullets, just in case. Maybe they only have a couple each, in the top of their magazines.
This makes Batman and his skill set the only viable option to save Martha.
It also eliminates the "why can't he find his own Mother" defense. He can, he just can't get to her.
Lex could have explained this straight away on the rooftop, before his crazy philosophical rant. It would have given a reason for Superman to stand impotently, listening to his rant afterwards - because he's waiting to find out what it will take to get his Mother back.
It also gives him a plausible reason to not kill or incapacitate Batman immediately at the start of the fight, because he wants to use him to save Martha.
There's ample precedent in the comics for this scenario.
Yet, the very obvious and logical question of why didn't he simply take Martha first never even seems to have been considered by Snyder.
No wonder they can't set up a simple rescue in a way that the reasons it plays out are even slightly believable.