Question 彼女が私たちのチームの選手だったらいいのにな

[Zizka]

In the sentence above, there are three ending particles: 「のに、な」I understand な has some emphatic connotation but what about のに, what purpose does it serve in the sentence?

 

[Toritoribe]

のに is an adversative conjunction, and it expresses a wish which is impossible/hard to be realized when it's put at the end of a sentence. Thus, it's close to subjunctive past in English.

空を飛べたらいいのに（でも実際は飛べない）。
I wish I could fly (but actually I can't).

 

[Zizka]

のに is an adversative conjunction, and it expresses a wish which is impossible/hard to be realized when it's put at the end of a sentence. Thus, it's close to subjunctive past in English.

空を飛べたらいいのに（でも実際は飛べない）。
I wish I could fly (but actually I can't).

What purpose does the いい here? What role does it play?

As for ～たら my dictionary says it's a conjunction which indicates that the action/state expressed by the main clause in a sentence takes place after the action state expressed.

先生に聞いたらすぐ分かった。
I understand how it works in this sentence ↑ but I don't understand what role it play in the original sentence.

 

[Toritoribe]

たら is a conditional here, so it's "it's good if~". As a result, ～たらいい is used as a set expression to express the speaker's wish/hope. I believe this expression is most likely in your dictionary.

 

[Zizka]

There are only three definitions for ～たら in my dictionary. The one I've mentioned, and ～たらする (do things like) and たらどうですか (why don't you). The only ～たら explanation which looks like a conditional is the one I've provided in the sense of:
先生に聞いたら→すぐ分かった。
When I asked my teacher I understood right away.
...which could be interpreted as a conditional I suppose.

So this: 空を飛べたらいいのに
Is meant to be interpreted as:
空を飛べたら→if I fly in the sky, いいのに, it is good.

 

[Toritoribe]

So this: 空を飛べたらいいのに
Is meant to be interpreted as:
空を飛べたら→if I fly in the sky, いいのに, it is good.

It's for just ～たらいい. のに shows it's impossible or hard to be realized, as I wrote.
e.g.
一緒に遊べたらいいな (expressing the speaker's wish, which might be able to be possible)
一緒に遊べたらいいのにな (expressing the speaker's wish, which is impossible or hard to be realized)