Hallo! I heard this weekend that both ways exist and I was really surprised, because I only knew ‘zu Hause’ in like “Ich bin zu Hause” for example (I am at home).
Could somebody help me understanding why and please also tell me if the meaning is then changing in ‘zuhause’? Also, are there other words working like this?
Danke im Voraus 
Prepositional phrases with “Hause” are generally written separately.
Ich bin zu Hause
Ich will nach Hause
In the moment you talk about your home as a noun, “Zuhause” is capitalized and written in one word:
Das ist mein Zuhause
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Danke Anne for your quick answer 
Then I can translate “Das ist mein Zuhause.” by “That’s my home.” ?
yes, that works …
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By the way: Whenever you have questions about grammar or words, this page will be helpful: https://www.duden.de/
It’s our “German Language Bible” 
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Or you just do like the Bavarians/Austrians/… and say heim/daheim, saves you the trouble of spelling 
- Wann gehst du heim? - Ich gehe jetzt heim.
- Wo bist du? - Ich bin daheim.
So much easier!
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