"David, you are a man."
Translation:David, du bist ein Mann.
Why must Mann Be a capital letter?
Because it's a noun. All nouns are capitalised in German.
This is so fundamental that it's mentioned in the tips and notes for the very first lesson unit: https://www.duolingo.com/skill/de/Basics-1/tips-and-notes
Please always read the tips and notes before starting a new lesson unit -- to do so, go to the website https://www.duolingo.com/ and click on a lesson unit, then on the "tips" or "lightbulb" button (depending on which you see):
I think the corret answer should be "David bist du ein Mann".
Because the phrase starts with David
No. David is set off from the main clause with a comma. It is not part of the main clause and doesn't influence the word order in the main clause.
David bist du ein Mann?
Here, too, you would need a comma to set off the name of the person you are talking to.
So bist and sind both mean 'are'?
Depends on what the word "mean" means.
"mean" = "have exactly the same meaning / range of meanings as" ? Then no.
"mean" = "can be translated into" ? Then yes.
du bist = you are
wir sind = we are
The choice depends not on the English word ("are") but on the subject pronoun, e.g. du versus wir.
So you can't say that any of those words are "the German word for are". German is not a code for English.