‎Which is correct?
1) I really (must/ have to) practise my piano. I'm not making any progress.
2) my sister (must/has to/mustn't /doesn't have to) wash the dishes. It's not fair.
3) our teacher (must /have to) take the register every morning to check who is at school.
4) you (must / have to) read his latest book. It's his best one.

See a translation

In all cases you can use either “must” or “have to” (#3 would be “has to”).

I usually hear “must” in more formal cases, or to order somebody to do something.

I usually hear “have/has to” in more informal cases, or when making a suggestion (although “must” is also occasionally used for this purpose too).

Overall I hear “has/have to” more often than “must”

2) If you are upset that your sister is NOT required to wash the dishes, you would say “must” or “has to”. I would also say “it’s not fair otherwise.”

If you are upset that your sister is required to wash the dishes, then you would use “mustn’t” or “doesn’t have to”. I would also say “it’s not fair to her”.