"Let's go and have lunch together!"
I am Chinese. The sentence you made is right. Just like English sentences "we go for lunch together" and "go for lunch together". We will get the same meanings.
I got marked wrong for 我们去一起吃午饭吧 Is that really wrong or should I suggest it be added?
吧 is modal particle. It always placed at the end of requests / commands.
No strict rules on having it here, but it will be more native on having it.
I don't agree with it. If 吧 is taken out from the sentence, it still have the meaning of "let's".
What about this: 我们去吃午饭一起把? Is the words "一起" must be before verb or what??
If you say that to a Chinese, he/she will know what you are talking about. But they won't say it in that way, or I mean it's not native.
The structure of Chinese and English is difference. In English, we can say "Let's go and have lunch together!" but in Chinese we won't say "我们去吃午饭一起吧？", we will say "我們去一起吃午飯吧"/ "我們一起去吃午飯吧".