The haircut shops near me have mostly women cutting the hair. Can I let a female cut my hair?
The answer is yes if these persons are married or mahrams there's no harm in doing so for the hair of the head. (The matter for married people is discussed in this fatwa in Arabic islamweb #176041)
Else it is not permissible.
The mahrams are basically quoted in (24:31):
... not expose their adornment except to their husbands, their fathers, their husbands' fathers, their sons, their husbands' sons, their brothers, their brothers' sons, their sisters' sons, their women, that which their right hands possess, or those male attendants having no physical desire, or children who are not yet aware of the private aspects of women. ...
A woman may cut the hair of another woman (by hair I mean all kinds of hair not only that hair of the head only), but there are limitations based on the limitation of 'awrah between women or between women and men. Some of this is covered in the fatwa islamqa #13744.
In summary when cutting the hair in general the rulings of 'awrah must be respected, if a person is allowed to look or touch the hair it is allowed if not it is forbidden.
See also islamqa #22841