... whether it is possible or not?
Yes! I actually feel this is MORE correct. When we are talking about alternatives ( eg 'I don't know whether I should go out or not') it sounds much better to me than 'if'.
"Doesn't matter if it's possible or not." should also be accepted and is a better English translation.
"it's not important whether it's possible or not" - not accepted
Would the following make sense?
"Não importa se for possível ou não"
I think "No matter" should be accepted.
I agree! Whether it's possible or not is just a more correct use of English.