A fish out of water is in an alien environment. If you say that someone is "a fish out of water," then you are saying they are out of their element. Stan the accountant was a fish out of water at the plumbing convention.
A square peg in a round hole.
I have bigger fish to fry is an idiom. An idiom is a phrase that is commonly used in certain areas that may have a funny meaning.
The reference to "fish" in a conversation could be a euphemism to change the topic or introduce a non-sequitur. Similarly, the idiom "like a fish out of water" describes feeling uncomfortable or out of place in a particular situation.
to have more important things to do
This is not an idiom. Idioms make little or no sense unless you know the definition. This sentence makes perfect sense, so it is not an idiom. The dead fish smelled so bad that even as high as Heaven, you could smell them.
It makes perfect sense, so it's not AN idiom.
"Głowa ryby", if what you write is not a kind of an idiom
This is not an idiom I have ever heard. Perhaps you mean water cooler talk, which means chat that might occur between workers at the water cooler or anywhere else.
It means that the thing which is being referred to is totally unnecessary, just like a bicycle is not needed by a fish.
If you think about this, you can figure it out. If fish are trapped in a barrel, how could they get away from a gun? It means something is ridiculously easy.
First, when you see the phrase AS ___ AS ___ it is A Simile instead of an idiom. It is easy to figure out the meaning of a simile. Water flows quickly, so the simile means that whatever it is, it's as fast as water flowing.