Correct translations for this sentence are both "I walk, you run, he sits." and "I am walking, you are running, he is sitting."
Is there any way in the Hungarian language how to differentiate between present and present continuous (resp. are there theirs equivalents)? Or there is just present tense, which can be used as an present continuous if needed?
No, there is only one present tense. If you want to say that he's running right now, you can say "Ő /éppen/ fut."
Pretty sure ő is either he or she, and is determined by context. So either he or she is sitting is technically correct since we have no context.
what is the difference between walk, stroll an go? To me it says the same thing. The programm tells me that go is wrong, sorry i cannot understand that.
'go' is a general term. There are many ways to go. You can walk, you can run, etc. In the sentence here we are listing different kinds of going: walking, running. So it does not make sense to use 'going' in place of 'walking' here.
It looks they do not want you to use different forms in the same sentence. I wrote: "I am walking, you run he sits" and got it wrong.
So I assume you write everything either in ING or normal present tense but not a mix.
I wrote "I am walking, you are running, he is sitting down": Rejected. Why?
I think the Hugarain means that he is sitting = in a sitting position, rather than that he is in the act of taking a sitting position.
If so, the problem with your sentence may be the word down, which suggests the act of sitting.