"Do we want to order a banana cake?"
In English, there is a difference between "do we want to order a banana cake" and "do we want to order banana cake".
Wouldn't 我們想点一块香蕉蛋糕嗎 be a better translation than 我們想点香蕉蛋糕嗎? (assuming the current English source is intended)
Also, do we have to use 要，or does 想 work as well?
English articles are usually not translated into Chinese. You would only specify "一个” in Chinese if you wanted to emphasize "one". It is not wrong to include "一个," but it shifts the emphasis and it is definitely not necessary. Also, ”一块” means "one piece". I think that an entire cake would use ”一个.”
My wife is a native Chinese speaker. I showed her my translation and Duolingo's translation: "我们想要点香蕉蛋糕吗？" and "我们要不要点香蕉蛋糕？" respectively. She said that, not only was my translation correct, but Duolingo's translation was awkward and less likely to be used by native speakers.
It means "order". In most situations (just like English) it would be understood without stating it. "Do we want to order cake" vs "Do we want cake". But I can envision some situations where adding it would avoid confusion: you're at home and say "do we want cake?" You might get the reply "I didn't know we have cake in the house"
I guess the question was written by someone from mainland China. In Hong Kong, where Cantonese is spoken, 点 is seldomly used. You are right, for all intents and purposes, 点 is colloquial. On the other hand, it is so prevalent. You better get used to it if you want to order some food in China.