"David, you are a man."
Translation:David, du bist ein Mann.
Neither of those -- it should be David, du bist ein Mann (with ein rather than 1 or eine).
No, because ihr seid is used when you speak to several people, but David is just one person.
Also, the noun Mann has to be capitalised.
Because you have to use the verb form which matches the subject.
Here, the subject is du, and du always goes with bist.
bin is the verb form for ich.
ich bin, du bist, er ist = I am, you are, he is.