What's the difference between "Ní hea" and "Nìl"? Both mean "it isn't", don't they?
They're not used in the same circumstances. Níl is used (when in the same sense as Ní hea) to answer a question regarding tá/an bhfuil in the negative. Ní hea is used for the copula.
An dochtúir é Pól? - Ní hea
An bhfuil Pól fuar - Níl
Isn't "ní hea" often used alone as a negative response, basically meaning "no"?
Ní hea is used as a negative response to questions that use the copula - An bainisteoir é Pól?, An Rolex é sin?, an domsa é sin?
You can't use ní hea as a response to questions that use the verb bí, or any other verb - an bhfuil tú sásta?, an itheann tú arán?, etc.
So you can't just stick ní hea in where ever you might use "no" in English.