You're looking at it from a comic angle now, Clark keeps his powers when not in direct contact to yellow sun radiation since his body can store the energy like a battery, but he will eventually need to recharge.
Film version, they need to be in direct contact to yellow sun radiation (YSR), at least from what we've seen. I wouldn't be surprised if Clark becomes a solar-battery like his comic counterpart in future films
Again, Zod and crew weren't surprised YSR gave them powers since it was knowledge Krypton previously had and Zod being general of the planet would likely have been privy to that knowledge. Jor-El comments to his wife "how?", when she mentions that humans would tried and kill Kal out of fear. Meaning Jor-El knew what YSR would do to Kal's biology
The suits did nothing to prevent solar radiation absorption, this is why they were powered, it did prevent sensory overload though
Here:
"Kryptonians within their natural environment are known to be as weak as a Human and are known to live within an atmosphere that would kill any Human, unless that Human is wearing a Breather. Kryptonians are also known to possess natural solar cells that allow them to process solar energy, which is what fuels their powers."
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Under their native Red sun, Kryptonians possess physical attributes similar to normal Humans. However, when exposed to solar radiation from a Yellow sun, Kryptonians gain superhuman abilities that greatly surpass those of humans and even most superhumans: DC Film Wiki
Notice it doesn't say: "Kryptonians have powers everywhere except under a red sun", as you seem to think