I think 'have to' should be accepted. It is the most direct translation and in English 'have to' means the same thing as 'supposed to' in the sense that someone is requiring you to do it...
I would only say 'supposed to' specifically if I had to do something but had not (I was supposed to do my homework but I didn't) or if something was normally one way but this time it was different (the train was supposed to come at 6 but arrived at 7)...otherwise it is faster to say 'had to' and to say 'supposed to'instead would be misleading.
it is the most direct translation
It is not. Have to in English means the same as must. In Czech it does not.
Do I have to do it? - Is it required that I do it? Is it my obligation to do it?
Am I supposed to do it? - Should I do it? Am I meant to do it? Is it a good idea to do it?
The two have a different meaning and the meaning of have to does not fit.
Have to does not necessarily mean the same as must! Have to relates more to duty and must relates more to a personal wish. of course mustn't means not allowed to do sth.
Both modal verbs can be used when talking about obligation. “Have to' is more common, especially in North America, but in the UK there is a subtle difference: 'must' is used for internal obligation and 'have to' is used for external obligation gle.com/search?q=have+to+and+must+difference&rlz=1C1CHBD_deDE868DE868&oq=have+to+and+&aqs=chrome.2.69i57j0l7.9160j1j4&sourceid=chrome&ie=UTF-8