Jan Mansour and Dave have given the literal translation, and yes, "nimm!" is the imperative form.
However, these sentences would typically be said while ordering food at a restaurant, and what you'd actually say in English at that point would be:
1. I'll have the omelette.
2. Why don't you also have the omelette? (the "doch" serves as a sort of qualifier here, to make sure it sounds like a suggestion, not like an order as would an imperative like "Sei still!" or "Geh weg!"
3. Let's have the omelette.
I think this is supposed to show you either how to use the imperative in German, or how English structures like "Let's..." and "Why don't you..." translate into German - or else you're supposed to learn how to order food in German :)
Gruss,
Susanne