They both mean the same. Some people may consider 'czemu' a worse option (a bit colloquial or a Russicism).
Why wouldn't "why are you going to the house?" work here as an alternative interpretation?
Hmmm... theoretically, Polish doesn't distinguish between home and house. I don't see many contexts where a sentence exactly like yours could be used naturally (without any additional information like: this house, that house, his house), but it doesn't mean that it's wrong. You can report it and see if the course creators accept it.
In English (at least US-Northeast), it's not uncommon to say stuff like "when are you going (back) to the house" instead of home (there may be SLIGHT differences in situational usage but they are inconsequential to meaning).
It's not a big deal, just wanted to make sure I wasn't missing something. Home works better in the example they gave anyway.
English doesn't use "to home". It's like an exception, because with (almost?) any other noun 'to' would be needed, of course.
Because in other examples, you would translate 'idziesz do XX' as 'going to XX' but saying 'going to home' is neither correct nor natural in English, you just say 'going home'. It's just an exception. Maybe an English native speaker can explain you better.
Hi, wouldn't it be possible to say "Dlaczego idziesz domu" excluding "do" with preserving the meaning? Another question, could this sentence as well mean "Why do you enter the house"? Like not saying going "to my" home, but to someones else's house or place. I know that wejść would be used as the "enter". I am asking because I am a czech. Czech and polish are quite similiar and so I am bit confused.
No, "Dlaczego idziesz domu?" makes no sense without 'do'.
In a proper context I guess that doesn't absolutely have to be your own home, but still, 'enter' is a different verb. That would be "Dlaczego wchodzisz do domu?" or maybe even better "do tego domu" (to this house).