There's a prequel comic where the committee on Superman analyses his heroic deeds and deduces his powers and what he's capable of (Lex Luthor also surreptitiously monitors these meetings).
So yes there's a whole government agency dedicated to figuring out what Superman can do. Probably not public knowledge, which is why Jenna Malone's character didn't make any connection between the bombing and Superman not stopping it.
This is it btw, all the prequel comics are great, gives you a deeper insight into the character and story:
http://imgur.com/gallery/gBmAz#Ol5XdpP
http://www.astortheatre.net.au/
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IIRC Batman's smoke grenades had the symbol for lead on them. So maybe there have been scientific papers on how Superman's X-ray vision probably works?
Also, this
:
http://www.imdb.com/board/bd0000130/nest/263626706

(EC) Lex gave him the chair, and the Senate exploded, long before he ever entered the Kryptonian ship

Why would the Kryptonian database have information about their powers? Jor-El just had a theory that he'd gain powers in a yellow sun, it's not like they routinely sent Kryptonians to other worlds to get powers then accumulated that data.
Zod and crew were honestly shocked to get powers and had no idea how to deal with them, hardly the reaction of a group that went to other worlds defending krypton.

Thanks to Batmeh v Supermeh Yawn of Justice, the "S" now stands for Sidekick

I assumed Lex found out about the lead by plundering the Kryptonian database. I figured that's how he found out about Supes's human identity as well. Although, that info could have previously been discovered by people snooping for weaknesses.
My IMDb lists:
http://www.imdb.com/user/ur5570856/lists?ref_=nv_usr_lst_3

Was it ever established in MoS or BvS that Clark knew he couldn't see through Lead?
NO. It wasn't. They expect you to be selfish enough to know all of that going in.

Vandalism is a pretty far cry from murder. Clark didn't even see him when he first walked into the room. Again, up until that moment, no one had done anything to make Clark suspect such behavior from anybody. You're asking him to be omniscient when he's not.
And who said he was smart enough to take out the Avengers?

His X-Ray vision isn't on 24/7 and he wasn't expecting a bomb in the first place. He has no reason to assume anything suspicious. Plus, the security guys were the ones who let Wally in. Why not blame them since checking for suspicious stuff is their job.
Hmmm. The guy who vandalized Superman's statue because he blames Superman for Wayne tower falling on him, is now sitting in a fancy wheelchair, IN THE COURT ROOM and this jack ass didn't think that was strange?
And this idiot is supposed to be smart enough to take out the Avengers?

His X-Ray vision isn't on 24/7 and he wasn't expecting a bomb in the first place. He has no reason to assume anything suspicious. Plus, the security guys were the ones who let Wally in. Why not blame them since checking for suspicious stuff is
their
job.

Because even though Clark isn't all powerful and all knowing, Lex thinks he is and took precautions. That's the whole point of the movie; that Clark is a person like everyone else despite his powers.

Well, it takes away some of Clark blaming himself that if he'd only been less self-absorbed he would have noticed and saved those people.
Also, this
:
http://www.imdb.com/board/bd0000130/nest/263626706

Didn't he say because he wasn't looking?
So if he's not looking, does it matter that the chair was made of lead? Like why even bother bringing that up?

He didn't investigate further because he didn't view Superman as a person but as an untouchable, malicious god who put himself above humanity. He was only interested in finding a way to kill him, but he didn't care about anything else beyond that.

Why would he think he has a civilian disguise?
Exactly! It's
publically known
this alien god-man was a drifter for years until he found his spaceship, NOW he'd start wearing a wig and fake beard and clock in at work somewhere to shoot the breeze around the watercooler?
Also, this
:
http://www.imdb.com/board/bd0000130/nest/263626706

"Secretly" doesn't mean he wears a mask or some kind of disguise. Secretly could easily mean "he just lived among you and acted like a an ordinary guy and blended into the background, never doing anything to draw much attention to himself".

Why would he think he has a civilian disguise? Some people here have even pointed out that Clark doesn't wear a mask as Superman so why would Bruce think he has a civilian disguise?
Oh I don't know, maybe because in MoS Zod broadcast to the WORLD on every device that would play video/sound that "He's been living among you, secretly".
Derp.

Thanks to Batmeh v Supermeh Yawn of Justice, the "S" now stands for Sidekick

Why would he think he has a civilian disguise? Some people here have even pointed out that Clark doesn't wear a mask as Superman so why would Bruce think he has a civilian disguise?
And this Batman is never referred to as "The World's Greatest Detective". Never mind how overblown that reputation has been for Batman as his detective work usually amounts to following blatantly obvious clues left by his enemies and beating up people for the right information if he's dealing with something more complex.

I've actually brought this up before and had someone tell me "Batman wouldn't care about that so wouldn't waste time looking into it"
So. you've sworn to attack and kill what many are calling an all powerful godlike being. and something like his civilian disguise and all the hidden treasures that go along with that, wouldn't be worth his time to even bother looking into?
are you fcking kidding me??
He'd look into every aspect and angle of his life he could find. the "Worlds greatest detective" would find aspects and angles Clark himself was probably never aware of but he can't be bothered to care about that??
I mean Lois figured it out pretty easily WITHOUT small hints like the aliens looking for Superman landing at the Kent Farm for some reason then a fight breaking out leaving an almost comical straight line path to Smallville for that fight.. I mean standing in smallville with a pair of binocs you could look through the 7-11 and see the fcking Kent front porch at the end of that straight line path of destruction.
But, he wouldn't care about that, couldn't be bothered to look into it during those 18 months of hate filled obsession. sure thing.

Thanks to Batmeh v Supermeh Yawn of Justice, the "S" now stands for Sidekick

Oh don't get me started on this! haha. I had almost a second video on this one thing alone, and it's been such a hammer blow in terms of destroying anyone's defence of this film.
Batman is a terrible characterization of 'The World's Greatest Detective', and in this universe his total lack of effort to find out anything about
the
most dangerous creature in the world, in his view, eradicates any believability to the character.
Lex figured it out. Lois figured it out. There is no explanation why someone
that
angry/fearful, with the resources at his disposal, would not have discovered who Clark Kent was. He would have combed through every single piece of rubble from Metropolis to Smallville, and easily traced all the 'incidents' in Clark's past back to the farm that the aliens trashed for some strange reason.
It's just stupid beyond words.

it just seems totally unlike the character of Batman to not investigate things.
Well this Batman had an 18 month obsession with "Superman" and didn't investigate him.
Lois figured out who he was following clues in a short montage in MoS. then the aliens that show up broadcasting that this alien has been disguised, living amongst us, land at the Kent Farm.. Clark then proceeds to leave a quite literal straight line path from the smallville fight to the kent front porch Lois Screams "Clark Clark" with cops around.. everyone in Smallville knew who he was, Pete Ross even did a double take when they crashed into the IHOP showing he plainly recognized him even after he'd been gone.
So Batman knows he's been here, living in disguise, he doesn't need to be a detective to figure it out, just use google, yet he's "Shocked" to hear "Martha"? he had enough info to track supermans life all the way back to the dog JK threw himself into a tornado trying to save FFS.

Thanks to Batmeh v Supermeh Yawn of Justice, the "S" now stands for Sidekick

Good point.

Didn't he say because he wasn't looking?
Yeah he though that he did not notice it because he was not looking then Louis informed him that he would not have seen it because it was lined with lead. Of course the reality is he still would have not noticed because he was not looking because I am sure if he noticed that he could not see though the chair it would have been a big give away that something was wrong. It is the lack of investigation into where he could have got the explosives from or the knowledge of how he rigged the explosive which is a glaring mistake. Surely when a terrorist attack happens in America they investigate where the terrorists got the equipment required to carry it out as standard practice and it just seems totally unlike the character of Batman to not investigate things.
To make a great film you need three things - the script, the script and the script -Alfred Hitchcock

Didn't he say because he wasn't looking?

Problem is Superman looks right at the wheel chair and never wonders why it's made of lead.
I mean a wheel chair made out of lead?
He should have known something was up. Plus he's Superman. Grab the wheelchair and fly out.