Form and rules
How it works
Have to often expresses rules or circumstances outside the speaker: I have to wear a uniform.
Must often expresses a strong personal obligation or a strong written/spoken rule.
Mustn't means prohibition; don't have to means lack of necessity.
Should/shouldn't gives advice or says what is a good/bad idea and is usually weaker than must.
Use had to for past obligation and will have to for future necessity.