Translation:This hospital has five hundred and sixty-three rooms.
You should actually not care about hyphens and punctuations right now, what you should really focus on is your speaking skills and I don't think that if you write sixty-three or sixty three does matter at all. So instead of wasting time where to put 'a' and where 'the' where a 'hyphen' where a 'comma' you should focus on your Turkish that do you get the meaning and if your translation is not WORD TO WORD accurate it doesn't matter because the main thing is that you understand.
I know check-writing has gone out of style, but the "most correct" solution is grammatically incorrect for writing numbers in English.
It should be "five-hundred sixty-three," with hyphens (I was marked as having typos) and without the "and", which is only supposed to be used preceding a fraction or decimal, i.e. five-hundred sixty-three and a half.
I am a native speaker and I would say the hospital HAS five hundred and sixty-three rooms. I have never heard anyone say any building IS WITH five hundred sixty-three rooms. The only similar construction I can think of that would be acceptable would be if it was phrased something like, "This is a house with X (bed/bath)rooms."