How do you say just 'children see cats' in polish as this means something a little different than "the children see cats" ?
I wonder what exact difference you have in mind... well, "the children" are some specific children, and "children" may be what, all children all over the world? But it won't change in Polish anyway.
You can use a habitual verb "widują" for "they often see", "they see from time to time", something like that. "Dzieci widują koty w każdą sobotę" would mean "The children see cats every Saturday".
So what does it mean? They are children or not? If they are, what children are they?
Without "the", they are any children. It would be a general statement. So there must be cats everywhere, if children generally see them. I suppose if you count books and TV, then it could be true. Children will at some point in their lives see cats, most likely - unless they live in a remote village with no books and no TV and there don't happen to be cats around.
did you know learning when to use "a' vs "the" is one of the things non-native english speakers struggle with the most, assuming their language does not have a similar article system? I used to think that was weird but then I realized that it really is a concept that's difficult to grasp if you didn't grow up hearing it. "the child" is supposed to be like, a specific child. But every child is a specific child? If I say "A child sees a cat" I'm talking about ONE specific child somewhere in the world, or maybe about a hypothetical child, or maybe a anecdotal child, but it's still one specific child. There are apparently like, upwards of 30 rules about when to use the vs a. crazy stuff.
Anyway polish doesn't use either of them. All languages have inherent ambiguity built into them, they're all subjective and require contextual interpretation to function.
In "A child sees a cat.", the child is not specific. Every child is not specific. Yes, there is not more than one child, but if we were talking about one specific child somewhere in the world, then we would say "One child sees a cat." or "The child sees a cat." I was not explaining Polish which I know does not use either "the" or "a"/"an". I did not say "every". For generalizations, in English we also us "a"/"an" to mean "any" child. This is important to know, because in some languages, such as French, the definite article is used for generalizations. So, the Polish sentence must simply accept a translation to English both with or without the definite article for a plural word. There is a difference between "any child anywhere" which is indefinite and "every child everywhere", but different languages use one or the other.
Do verbs need to agree with their performers? or do they just follow point of view and number? (first person singular, third person plural, etc)
Verbs need to agree with the subject of the sentence. (I don't understand what you mean with performer vs point of view).
In all tenses verbs change with person and number. In the past tense they also change with gender of the subject. In future compound you choose if you want to use forms that show gender or not.
Sorry, my question was poorly worded and I couldn't think of what you call the thing that does the verb. I meant to ask if verbs had to agree with their subject in any ways beyond number and person. So they only have to agree with gender in past tense? That's wild.