I’ve to do lots of things today.
I have to do lots of things today.
I haven’t to earn a lot of money to be happy.
I don’t have to earn a lot of money to be happy.
Have you to get up early tomorrow?
Do you have to get up early tomorrow?
In have to, have is a main verb, not an auxiliary verb.
We do not normally contract it in affirmative sentences: I have to, not I’ve to.
Use do/does in questions and don’t/doesn’t in negative sentences.
Don’t have to means that something is not necessary: ‘You don’t have to come if you are busy.’
With have got to, we can contract have: ‘I’ve got to leave now.’