"Noi ne iubim unii pe alții întrucât suntem o familie."

Ne means "us"/ "ourselves", never "neither".

Romanian uses pronominal reduplication a lot (which is similar to that in Spanish), involving the employment of clitic pronouns in verb phrases together with the full noun phrases that they refer to.

Here is an example in the dative case:

• Îi dau un cadou fratelui meu. = I give a present to my brother. (lit. "Him I give a present to my brother.")

You can see that the dative pronoun îi doubles the dative noun fratelui.

And another example in the accusative case:

• Îl respect pe profesorul meu. = I respect my teacher. (lit. "Him I respect my teacher.")

Here the accusative pronoun îl doubles the accusative noun profesorul.

As for the Romanian word for "neither", it's nici. "Neither... nor..." is simply nici..., nici....