It's an interesting thing to think about, sure, but even I have to get to a point where the nitpicking - which is really what this works out to be - has to prompt a reaction similar to "Ok, enough's enough, that's just being ridiculous now."
I'm
not dismissing this however because I'm about to point something out that goes along with what you're saying so bear with me as I explain it (or at least how I've explained it to myself):
Kal's been on Earth for 33+ years, he's been exposed to our sun the whole time and breathing in our atmosphere (the two components that give him his powers, as we now understand it from this telling of the Superman tale - nothing that came before this movie matters except maybe the prequel comic but that's something that not enough people have read, I suppose).
Anyway, inside the Black Zero Kal reacts rather violently to being exposed to a Kryptonian atmosphere for the first time in 33+ years - he
was born into such an environment so his body
does have experience with it (as a baby for a short period of time). Pretty sure the craft that he came to Earth in would have maintained that atmosphere as well (but there's no way to know for certain at this point - it
could have actually slowly acclimated Kal to what he was going to be living in once he got to Earth; Jor-El had all the data about Earth necessary including knowing that Kal "would be a god to us" basically and that's because of info provided by the scout ships many years past, this is prequel comic material that I'm hinting at).
The prequel comic makes it clear that Krypton is well aware of Earth and our sun, known as Sol, because Kara is shown (again, in the prequel comic) making the statement that our system, the Sol system, was never an intended destination for her scout ship or any others - it's already inhabited by humanity (even 18,000+ years ago) and the Kryptonian expansion and them spreading their civilization far and wide did not happen by wiping out races and species and planets that were already teaming with life forms as our planet was.
Anyway, the point I'm getting at in this long roundabout way is that we only see one direct instance of a Kryptonian using a "super power" inside the Black Zero. Do you remember what it was?
It was the girl who was trying to stop Lois from escaping when she punched a hole in the wall of the escape pod - at that moment her helm is active (her head is protected and she's breathing a pure Kryptonian atmosphere - she's not exposed to the now altered Earth-like atmosphere Jor-El's consciousness has created inside the Black Zero).
The rest of the time inside the Black Zero everything is somewhat normal: none of them use super-speed to catch Lois when she's out and about - they chase after her slowly, walking even, hoping to shoot her with their Kryptonian ray guns more or less.
That's the only instance of a Kryptonian using a "super power" inside the Black Zero - and it takes a cue of sorts from a panel in the prequel comic as the scout ship comes into range of our sun: Dev-Em (don't ask) throws a punch at Kara and she steps out of the way; Dev-Em suddenly wonders why his punch hits the inside wall and yet his fist seems to have punched itself clean into the material leaving his fist-print. In other words, they're inside a Kryptonian scout ship, it's full of Kryptonian atmosphere because of the Kryptonian life support system (they haven't reached Earth yet), and because they're in range of our sun (prominently featured in several panels of that prequel comic, larger than life to some degrees) Kara and Dev-Em are already experienced alterations but only Dev-Em actually does something to demonstrate it by punching his fist into a wall.
So, here's my take on these situations:
- inside the Black Zero the Kryptonians developed
at least super strength from being exposed to our younger yellow sun's radiation
- as for other powers, we simply don't know for sure but we do know that when the Kryptonians come down to our planet they show that they have super strength and super speed (they somewhat go hand in hand, it's not like they'd be able to zip all over the place like Dragonball Z characters if you stripped them of that super strength -
the speed is directly linked to the strength) - also, super strength is directly related to gravity as well as yellow sun radiation
- we see Zod as the first to be affected by our atmosphere in terms of
other powers in that when Kal basically uses his helm like a punching bag and then face plants him into the 7-11 and then the pavement, it causes his helm to malfunction and Zod is exposed to Earth's atmosphere directly, which causes two powers to manifest in a matter of moments: X-ray vision and super hearing, and that's all we see but there's a third power he displays if you're paying attention: he's invulnerable and undamaged (meaning Zod personally, not his armor/helm) but that's because of the yellow sun
not the atmosphere
- Kal, having been raised here, is affected by the Kryptonian atmosphere inside the Black Zero to the point where - from our perspective as viewers - we see him lose two powers directly: first is super strength since he can't manage to break the straps holding him down to that examination table, and second is his invulnerability because Jax-Ur has no issues whatsoever penetrating Kal's skin to take that blood sample. It's
assumed at this point that Kal is totally and completely powerless, but it's not a 100% certainty since we only see the direct effects as those two powers not being functional
- Kal's exposure to that Kryptonian atmosphere doesn't last very long, we don't know precisely how long but we can assume that he's in process for adapting to it
if he were inside that ship long enough just as those Kryptonians had adapted in the sense that they were currently and had been living in that atmosphere for 33+ years so the powers they were manifesting by being under our yellow sun were invulnerability and super strength/speed,
the exact same powers Kal has because of the yellow sun. The other powers demonstrated in the movie -
hearing, X-ray vision, and of course everybody's new fave, heat vision - all come from being exposed to our atmosphere, apparently. There's one other power that I believe Kal demonstrates but they don't cover it with a CGI effect: telescopic vision, which Kal uses to see into the escape pod, but this is my assumption because we don't see some telescopic effect, maybe they actually did some CGI work on that and it'll be in the DVD/Blu-ray, who knows but when Jor-El says "Look" it's pretty obvious that Kal looks and then can see who it is - of course he might be making an assumption about "Who would take an escape pod to get off this ship back to Earth, oh yeah, gotta be Lois."
Funny thing is that not every Kryptonian came down to Earth during their time here so there's a very
very strong possibility that some of them inside the Black Zero never even realize they have any kind of powers - Zod may not have told them. Of course, again as I noted in the beginning of this post, sometimes we take these nitpicks just a wee bit too far.
tl;dr version:
Kal's powers manifested by yellow sun radiation coupled with Earth's atmosphere: even Jor-El tells him this during the scout ship chat. Kal even asks "Why am I so powerful?" (a lot of people miss this question since it's at a point where the music kicks in but as he's walking outside the scout ship he asks - we're hearing dialogue from the chat which obviously has happened earlier since a) Kal is now wearing the suit and b) he's got a nice clean shave.

) and Jor-El tells him it's a combination of the younger yellow sun's radiation as well as our atmosphere, a one-two punch if you will.
The Kryptonians arriving here have at the bare minimum super strength/speed and invulnerability just from being exposed to our yellow sun's radiation. Couple that with direct atmospheric exposure and other powers manifest (hearing, X-ray vision, heat vision, and potentially telescopic vision as well if my assumption is correct on that one).
Does this cover at least some of your questions?
I do have an issue with one aspect: gravity. The belief is that Kal is strong because of the weaker gravity here on Earth to some degree and I agree with that but but but...
Kal came here as a baby, he's never really been exposed to the much stronger gravity on Krypton except for that brief short period after being born and then sent to Earth (again we don't know how much time that was from birth to launch, days probably, or less). Anyway, it's understandable that's it's used in some respects as part of the explanation for the super strength but but but...
Zod and his crew have lived on Krypton, and now they've been living on a Kryptonian ship for 33+ years which would obviously maintain a Kryptonian atmosphere which we can safely assume would duplicate
even the gravity of their home world to some degree which would give them a slight advantage in terms of strength over Kal. Anyone that's seen DBZ knows the part of the series where Goku trains in that device which increases gravity over time and obviously makes him much MUCH stronger because of it so...
Kal = been living here under our weaker gravity for 33+ years, is used to it, shouldn't be a factor in his strength after that period of time
Kryptonians = just show up and are put in a much lighter gravity environment when on Earth, it's surprising they don't just literally float when walking.
Also this truly baffling screw-up (just kidding):
If the Black Zero is providing a truly Kryptonian living environment which again obviously means it's stronger gravity than Earth, that should mean when Kal and Lois come on board
at least Lois would have been barely able stand considering the much stronger effect of Kryptonian gravity.
Am I right or am I right?