I'm not sure whether "implication" is your choice of word or that of the textbook. Whichever it is, I'm not keen on it. I don't think any of those are implications - they're simply meanings.
"I'd like the menu" is simply another, and more natural, way of saying "I'd like you to give/bring me the menu".
I disagree that "Vegetables, please" (after being given two options) means or implies "Yes". The only possible answers to "And would you like vegetables or salad?" are "Both", "Neither", "Vegetables" and "Salad". If the person said "Yes" in response to the original question, it wouldn't be clear what they wanted.
"Can I have the bill?" is simply the standard way of asking for the bill. I've never heard anyone say "Can you give/bring me the bill?"
For me, an implication is different. If the waiter said "And would you like vegetables or salad? The salad's really good!", that would imply that he felt the salad would be the better choice.
On a separate note, it's rather odd for someone to order both the salmon and the steak for their main course. It's not impossible, of course, but it's unusual to order a starter and then two main courses.

English Teacher