How would you know if it would be the case?
I don't know whether I would. All I know is that I don't recall ever seeing or hearing her have difficulty that seemed to relate in any way to such things. Perhaps I wouldn't expect to have done; I'm not claiming this as strong evidence; as I say, I think we're both basically guessing.
The rest of what you say still seems to me to be guessing that there "ought" to be a problem. I agree that you've presented some examples of ambiguity, and when something can mean X or Y and you want to say specifically X or specifically Y that can make your life more difficult. But when something can mean X or Y and you want to say "X or Y" the ambiguity is positively helpful (your hand really is part of your arm, and I bet there are cases where ręka is strictly better than either English word). And needing to learn fewer words is nice. And using less language-space means better robustness against errors. And ambiguity is often beneficial in poetry. Etc., etc., etc. Maybe these instances of ambiguity really do make English (and Polish) worse languages than they would be if they were patched up. But I don't think you're in a position to say that they do just on the basis that they are instances of ambiguity.
Sidenote:
How would you know if it would be the case?
You would know because she would make errors. Kids don't stop talking because they don't know the right word. You know that irregular past tense is hard(er) for kids to learn because they say things like 'runned' and 'eated'. In some cases it might be a circumlocution rather than an error ('I'm the big one' in place of 'I'm the biggest'), but it's not hard to know what a kid is having trouble learning if you are paying attention.
I'm working on a conlang (constructed language) and would like some input from the Less Wrong community. One of the goals is to investigate the old Sapir-Whorf hypothesis regarding language affecting cognition. Does anyone here have any ideas regarding linguistic mechanisms that would encourage more rational thinking, apart from those that are present in the oft-discussed conlangs e-prime, loglan, and its offshoot lojban? Or perhaps mechanisms that are used in one of those conlangs, but might be buried too deeply for a person such as myself, who only has superficial knowledge about them, to have recognized? Any input is welcomed, from other conlangs to crazy ideas.