So would this sentence change, for example, in response to your friend asking if they can take some of your food?
Yes, that would be a good example.
A polite phrase that children learn as part of table manners is kan jag be och få saltet/smöret/potatisen (roughly ’may I ask to have the salt/butter/potatoes’).
My Spanish knowledge is extremely limited, but based on my (small amount of) research, I think you're correct. Anyone else reading this that knows Spanish better, please correct me if I'm wrong!
"Need you really ask" may be a seldom-used format, but it should still be acceptable (see "need I remind you" for a common usage of the format).
I put "do you need to really ask?", which, I know, sounds a bit clunky in English and so I get why it's counted wrong. In this situation though, how would you know which verb the adverb qualifies?