"She shows us."

Translation: Ea ne arată nouă.

[MicahFerguson]

Is the noua necessary?

[potestasity]

Generally no. What's strange is that it affects the meaning of the sentence. The English sentence is ambiguous, she could either be showing us something or showing us to someone. That ambiguity is kept in the Romanian sentence "Ea ne arată."
But, "Ea ne arată nouă." can only mean that she is showing us something.

[Motanu11]

I agree with your last translation potestasity. Otherwise, what is it doing in a lesson on dative pronouns. A diagram of the English sentence would depict only a subject (nominative), a verb and a direct object (accusative) -- No indirect object, no dative case. If however your last translation is assumed, then the English sentence should have been, "She shows us {something}. Then, {something} would be the direct object (accusative) and "us" would be the indirect object (dative).

[splittongue]

great explanation potestasity, "gând la gând cu bucurie!”...

have a lingot...

[PaulMinden]

Great explanation -- multumim! Out of curiosity, could 'ea ne arata noua' also mean "she shows us ourselves'? As in, she (perhaps a psychiatrist?) is helping us take an introspective look at ourselves?

[Elena_Bostanica]

Technically yes, but it sounds very, very unnatural and it's highly unlikely that you will ever hear someone say that. I would rather use the verb "a descoperi" ("to discover") to get that meaning. For example: "Ea ne ajută să ne descoperim" (She helps us discover ourselves).

[KevinSmith777042]

How to decide not to put the Noua( at the start?

[NicoGiuliani]

Is the sentence, "Ea ne arată pe noi" acceptable?

[splittongue]

yes, see potestasity's great explanation above, ”ea ne arată pe noi (cuiva)” would mean ”she shows us (to somebody)”, as opposite to ”ea ne arată nouă (ceva)” which only means ”she shows us (something)”. That is because ”pe noi” is accusative, and ”nouă” is dative. Anyhow, we are here in a dative lesson...