Usually a question tag is formed from the modal of the main statement. (Where a positive present tense is used the modal is 'do'. e.g. 'He comes to school on Mondays, doesn't he?')
With 'have' and 'do' there is a problem because these are both modals and actual verbs.
So when we say 'Peter has no car' most English users would simply use 'has he?' in the question tag, because it 'sounds right' even though the correct usage would be 'does he?' (We use a positive question tag because the 'no car' is negative.) More probably an English speaker would re-phrase the sentence to say 'Peter doesn't have a car, does he?' to avoid the problem altogether. (English speakers do this all the time without realizing they're doing it.)
The second use of 'have' is in a longer sentence, so the listener has more time to figure out that 'have' is a verb and most people would correctly say 'You have brothers and sisters, don't you?'
'Mustn't' in a question tag reply is more of a problem because 'mustn't' means 'it is forbidden to do this' as in 'you mustn't be unkind to old ladies'. So if you say 'I mustn't sweep the office' this does not mean you do not have to, but that you should not.
This changes the meaning of the reply from 'No, I do not need to' to 'Actually, I am forbidden from doing that'. So here an English speaker would answer the meaning of the question, even though he has to change the modal of compulsion to do so. So with the last two queries, the correct reply is 'No, I needn't' though most English speakers would probably give you a full sentence as a reply in order to be clear.
e.g. 'We must be at home at 6pm, mustn't we?'
'No, it's not compulsory.'