As far as I know, this one is a tricky one: "venite!" is for the 2nd plural imperative: (You all) come! 2nd singular would be: "Vieni!" "Come!"
"Venga!" is however 3rd person singular ("he shall come!") which is used in this context as a formal you: "(Sir,) Come!
I'm sure it is explained in more details elsewhere, but here it might be enough. It also make senses to examine a bit full conjugation tables (Imperative column) to understand better. You will find a good one here: http://www.italian-verbs.com/italian-verbs/conjugation.php?verbo=venire
Your question is a bit unclear, but as SamMWBlake has answered parts of it, I'll try to answer the rest.
The Italian infitives I've seen so far end in either -ere, -are or -ire. You may also find infinitives being used as negative imperatives, e.g. "Non venire qua!" ("Do not come here!").
I have never understood why Duolingo does not indicate whether it should be singular, formal or plural when translating from Italian to English. Since the word you can mean all three, this is very confusing. Is there a discussion about this somewhere? (By the way, same problem with Google translate)