Student or Learner
When you're at a restaurant asking for a menu, correct expression would be:
Can I see a menu, please? or Can I see the menu, please?
Can I have a/the menu, please?
I'd like a/the menu, please?
Also, when want to ask your server to let you keep the menu for a while longer, what can you say? Something like, "Can I/we keep the menu?" or "Can you leave the menu here?" Let me know the expressions you'd normally use.
Actually, all of the phrases you listed as ways to ask for a menu are correct. I don't understand why you would want to read the menu for awhile longer if you have already made your selections. If you ask to "keep" the menu, after you have ordered your meal, they may think that you wish to take it home with you. If you want to keep the menu at your table because you haven't made your selections, then you could say, "I need a bit more time to decide, please."