So,they became reality warpers, but their human minds weren't ready for such power. Couldn't they just wish themselves into being able to hold such power?
Except that's now how the Sphere works. All it does is unlock a part of the human mind and abilities that people already have, but can't normally access. The Sphere isn't so much a Literal Genie as a key, and that still leaves the problem of their minds not being able to handle it just because of the way they're built.
Short version is that they can't do anything, just almost. Therefore they couldn't improve their own levels of comprehension.
It's also a matter of responsibility. Even if they could control the powers, they'd be the only three people in the world with omnipotence. That would completely destabilize life on Earth as we know it. It might be cool in the short term, but it could certainly turn into a nightmare of epic proportions. Our conscious feelings can manifest things just as if not more horrific as our subconscious can. Worse, what would happen if everybody in the world wanted a crack at the Sphere, or the military tried to weaponize it?
If the letters J and E were mistakenly substituted for H and A in the cipher, why was Harry the only word affected in the translation instead of every word containing those letters?
I think the implication was that he mistranslated it deliberately and just changed those letters to avoid implicating himself, since he figured out what was going on since he'd been in the Sphere by that point. That or the time in the Sphere made him forget and he simply didn't want to acknowledge that it was really him so he subconsciously changed it.
The way the code works is shown, every two number combination gets translated as a single letter. If A and E were switched around in one place, they would have been switched around in all places, not just in one specific word. This means that "Stop calling me Jerry" would actually appear on screen as "Stop celling ma Harry!" (Unless of course the character managed to sneak in a subroutine for replacing every "Harry" with "Jerry" and the reverse but only when communicating in the opposite direction within a few seconds while everyone was watching.)
At one point in the film, Dustin Hoffman's character was forced to leave the lab and go into the water without a suit. Beth warns him he'll freeze. Wouldn't the pressure of the water down there be enough to crush him?
No. It was already explained during their briefing that you could go out into the water and be perfectly fine. The pressure won't kill you - the cold will.
Specifically, they'd already been acclimated to the pressure (and why when they go back up they need to be in a decompression chamber) so you'd only get crushed if your body hadn't already adjusted to the outside pressure. So he was fine.
A lot of the technology shown in the movie actually uses this. The characters can dive out of a simple opening in the floor of their habitat because the air pressure is just as high as the water pressure, and the soft suits they use in the diving scenes would offer no protection from pressure whatsoever.