Non ho bisogno di te
So is "farlo" equals to "lo fare" or is one of them used more commonly? please clarify thanks.
«lo fare» is not used often. It is better to attach the pronoun to the end when the verb is in the infinitive or in any of the imperative conjugations.
Is this grammar something similar to spanish, like "ayúdame"?
You mean how the pronoun attaches to the infinitive of «farlo»? Then, yes. Pronouns can only attach to the ends of verbs in the infinitive and in the imperative, just like in Spanish.
I can manage without your help means the same and should be accepted, I reported
Yes, it means (almost) the same, but it's not stated in the same way. If you translate 'fare' as 'manage', that's not correct, at least not in the basic meaning that is required.
And "I can do without your help" should also be accepted,since there's no object in Italian
lo + fare = farlo