Is must the same as have to?

Often close. Must is usually your own strong feeling, and have to is a rule or a need from outside. Have to is more common in speech.

Can I say don't must?

No. Must does not use do. Say mustn't for forbidden, or don't have to for not necessary.

Grammar, compared

Must and have to are close. Mustn't and don't have to are opposites. Should is advice.

Must, have to / Mustn't, don't have to
Must, have to	Mustn't, don't have to
I have to wear a uniform. (A rule.)	You don't have to wear a tie. (Not necessary.)
You must call your mother. (I feel strongly.)	You mustn't park here. (Forbidden.)
She must be tired. (I'm sure.)	You should rest. (Advice.)

Must, have to and should compared
Meaning	Form	Example
Rule from outside	have to, has to	I have to work on Saturdays.
Strong personal feeling	must	I must remember to call her.
Forbidden	mustn't	You mustn't use your phone here.
Not necessary	don't have to, don't need to	You don't have to come.
Advice	should, shouldn't	You should sleep more.
Sure it is true	must be	He must be at work.

You don't have to is not the opposite of you must. It means you can, but you do not need to. The opposite is you mustn't.
Must has no past. Yesterday I had to work, not I musted.
Tengo que is usually have to. Debería is should.
Ask Do I have to? in normal speech. Must I? sounds formal.

Is must the same as have to?: Often close. Must is usually your own strong feeling, and have to is a rule or a need from outside. Have to is more common in speech.
Can I say don't must?: No. Must does not use do. Say mustn't for forbidden, or don't have to for not necessary.

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