'She hasn't to do this' is unusual and a bit dated, but is correct. It means 'She must not do this'. 'She doesn't have to do this' is also correct, but has a slightly different meaning - 'She is not required to do this (but she may if she chooses)'. So they are not interchangeable

I think, technically, you could use "she hasn't to do this", (although someone may correct me on this), but you're right - it does sound weird. "She doesn't have to do this " is the best way to say it.

she hasn't got to do this or she doesn't have to do this.

I agree with Jen. "She doesn't have to do this" would be the most accepted wording.

using haven't or hasn't is odd n uncommon. the best choise is ur second option