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"One way or another" is not an idiom - it means exactly what it says. If you are going to do something one way or another, then you are do whatever it takes. If one way does not work, you are going to try another way.
An idiom misuse is to use and idiom in a wrong way that doesn't make sense.
You either have your fingers on the wrong keys, or you are not speaking English. Either way, no it's not an English idiom.
"Be on the same page" is an idiom that means to agree or have the same understanding or opinion about something.
It is just an exaggerated way of saying something happens quite often - it is hyperbole, not an idiom.
This is not an idiom that I have ever heard. Perhaps you mean an arm AND a leg, which is an exaggerated way of saying something is really expensive.
It's not an idiom because you can figure it out. It's a sarcastic way of saying something is not clear - it's as dark as mud.
The best way to diagnose a problem is going to see your General Practitioner (Doctor).
It means that something is going wrong with them. The best way to solve is making lab testings.
If I do something "behind your back", it means that I do it without your knowledge, usually in a sneaky way.
Some do not know they are going the wrong way. Some know they are going the wrong way but can't help themselves because of other forces such as addiction.
Car going wrong way