I think the use about the word なる you said is right. But I am not so sure about the translation you did.
Firstly, no problem does not mean 大変じゃない, that sounds a little weird to me because in my opinion, 大変じゃない means it is not exhausting, I can still take it. For no problem, I would say 大丈夫だ, that means it is not a problem, it's ok.
And for "if that would make me rich", because there is this word make, I think it's better to translate it to する. So this sentence will be like "もしそれが私をお金持ちにしてくれれば、大丈夫だ".
As for your last sentence, was is the past tense of is, right? So it means である or です or だ in Japanese. There is no change, and it's just a condition I was in right? So it is not "become", and this sentence will be 私がお金持ちだったら/であったら/でしたら、大丈夫だった。
I hope this is helpful to you. Enjoy learning Japanese.