I'm finding Polish cases really difficult to get my head around. How understood can I be to native speakers when I get my cases wrong? My Polish friends are always correcting me, so I suppose they at least get the main point of what I'm trying to say?
It depends on the sentence, and context. Sometimes there is only one way the sentence should work, so when your friends know you struggle with Polish they understand you, even if that sounds like (I now be to speak language Polish gooder).
Sometimes when context is not clear and the same sentence can have different meanings.
Kasia gotuje mamie zupę. - Kasia cooks soup for mom
Kasi gotuje mama zupę - Mom cooks soup for kasia
Kasię gotuje mama zupie - Mom cooks Kasia for soup
Kasia gotuje mamę zupie - Kasia cooks Mom for soup
Kasi gotuje mamę zupa - Soup cooks Mom for Kasia
Kasię gotuje mamie zupa - Soup cooks Kasia for Mom
Of course most of the sentences are clearly wrong from context, and you can tell. But I would be careful with dative and instrumental.
Am I on the right track here?
If someone else and I were having a conversation.. If someone was speaking to me in English I would say "I hear you". "I am listening to you" would be the other option if I was paying attention. "I listen you" or "I listen to you" would both be awkward.
In regard to observing that person.. If is said "I see you", that works. If I said "I look you" or "I look for you", that would be awkward. "I am looking for you" would be best.
There seems to be more involved than just the physical observations. There is intention with look and listen. I believe that is what makes these verbs take the genitive case.
There are only three cases in modern English, they are subjective (he), objective (him) and possessive (his). They may seem more familiar in their old English form - nominative, accusative and genitive.
So in modern English, it seems that something must be done with the genitive case verbs to make a sentence grammatically correct and you have to add the first person singular "am", a past participle -ing and a preposition like "for".
Negative accusative: "I not hear you", "I not see you", would be awkward as well. "I don't hear you", "I don't see you" would be correct. "I am not hearing you" and "I am not seeing you" would be correct with more emphasis and/or habit. The sentence has to be modified to support proper grammar. With Polish, I believe there is no difference between present and habit e.g. "He drinks", "He is drinking" would be the same thing; "On pije".
With polish, you decline and conjugate to support the grammar. Which is what I am going to get back to now.
As immery nicely showed - wrong case will mess meaning of sentence but it should be possible to guess what you had on mind.
About correcting - do not worry, most Poles love to correct others and ask for saying something difficult like "Stół z powyłamywanymi nogami", "Cóż, że ze Szwecji", "Chrząszcz brzmi w trzcinie (...)", "Grzegorz Brzęczyszczykiewicz (...)"