There are many ways to make Batman (or Lex) realize that it has effects on Superman. If Superman isn't aware of its power over him, Batman /Wayne or Lex could be shown carriying a piece of it on themselves, and when Superman/Clark is around, he feels strange/dizzy/weak/etc. without understanding what's going on. Both Batman and Lex would be able to eventually do the 1+1 math. Batman could be told by Lex about it, or he could find out by himself. 

You should try to think a little further...

So Superman wouldn't recognize the exact same feeling being in Krypton's atmosphere had on him?  Lex wouldn't know either, btw.  And unless Zod brought some w/ him, or the World Machine made some, we're still stuck wondering how exactly shards of Krypton made it to earth w/in 20-30 years of Superman landing here.   AND if the World Machine created shards, it's actually more likely than not that Superman would notice the effects, given he probably helped in the cleanup.  Right?

Agreed with you. I think making the movie around that stupid fight is dumb as hell, make it a small skirmish like they did on the avengers or in Justice League: War, yes a lot of people want to see these 2 characters fight, but there is nothing at stake here, they will not kill each other, they will not even injure each other, and at the end they will be friends. They are both the good guys, Batman is smarter than to pick up a fight with someone who is helping people around the world, Superman (at least the one from the comics) is always trying to end things without a fight and will not battle just to see who is stronger.

Building a movie about a gritty comic of the 80's that is not part of the continuity does not make sense at all, and even in that comic the central part of the plot in NOT the stupid fight, there is another reason why they have to battle and even in that one Superman is trying to avoid it. Goyer is great writting many DC characters like Batman and Constantine, but he has no clue on how to handle Superman, he treats him like a 1 dimensional alien without any conection with his family or the world, that is almost stupid and has no real depth, he almost did not had any lines in MOS and it looks like is the same on this movie. Skipping it.

The effect might weaken him, but it may not make him feel the same exact same way as the atmosphere did in MoS. The bleeding and problem to breathe, for example, are most likely not going to be among the effects it has on him.

As for the rest of your questions, nothing tells us the rocks arrived later. 

If Superman can have omnicience, yes, Batman can have telekinesis.

But seriously.....what? You're...creative, I'll give you that.

Yeah, Superman has super-hearing...but nothing at this level. When he focuses he can hear a distant voice....that doesn't mean he can suddenly hear everything everyone is saying all the time, which is the only way he'd be able to do what you're saying. This isn't Silver Age Superman, you know.

As for how this weakness is discovered, that's something that we will need to wait for the movie for. They could very well simply run tests of the effect of Krytopinite on Zod's cells, and see some sort of "effect". Probably not scientific, but neither is heat vision or Superman's flight.

Woo, I have a supporter!  Hell yeah!  Agreed, both Batman and Superman are good people, and it's silly to think that when Superman doesn't crush Batman initially, that Bruce Wayne wouldn't stop to think about his course of action.  Neither Batman or Superman are idiots.

It's comic book tradition that the first meeting between Batman and Superman ends with them fighting each other, before becoming allies.

It wouldn't have to, anything resembling what happened to him on that ship would very likely make him perk up and pay attention, would it not?  Come on.  Superman is not an idiot. 

Nothing tells us how the rocks got there period, so right now it's all guesswork.  I was merely thinking about Krypton's location and since they nicely laid out where it is for me, I started thinking about the math involved here, and unless it was actually brought to Earth from Krypton (or possibly the remnants of an earlier asteroid impact w/ Krypton from thousands of years ago??? maybe??) there's no way shards of Krypton could make it to Earth, this quickly.  

Which brings back the World Engine theory, but, we know Superman was probably integral in cleanup and rescue efforts after the incident, it's extremely likely he'd notice the lingering effects, right?  So, no matter how you flip this, it's not like Superman shouldn't have advanced warning.

Ok, disclaimer then, as I said earlier I've never read the comics.  There's only 1 Superman comic I own, and that's the 'collection' of comics that all contributed to the 'Death of Superman' (which was just...one of the most brutal affairs ever).

Funny story though, Batman fought Spawn once, at least, he tried to.  I recommend seeing how that worked out, if you aren't already aware lol.

We've already established Superman isn't and has never been omniscient.  That would include the ability to hear peoples thoughts, and he's never (in any comic) had that power (I don't think, anyway).  So no, Batman having telekinesis (I think it'd actually be telepathy, wouldn't it?  Mind to mind talking?  My bad earlier if it is) would not only be ridiculous, it'd also completely change who Bruce Wayne is, and the entire life he lived up to that point.  Having a super/mutant power changes things.

As far as how sensitive his hearing is, I'd give you that, if I thought he was focused on his mother the entire time he was saving Lois from that malfunctioning life pod.  He was in mid-conversation with her and then suddenly boom, gone.  What is he always totally focused on his mom?  I mean, that's semi-believable, but I dunno.  Seems thin.

Also thin, thinking that Superman would allow humans to dispose of the bodies of the Kryptonians.   Not out of mis-trust perse (though, he has to know a bit about how the military functions at this point, so maybe being suspicious isn't outside the realm of possibility), but given how much it hurt him to kill them all, you would expect he would make a big deal out of the burials.