You seem to think in English. In English "give" can be Present Simple form of the verb used for all persons except the third person singular (for which you use "gives"), infinitive but also an imperative. In Polish each of these forms has its own morphology and they look clearly different. Here you can see an imperative form of the verb "dać" which is used for second person singular. There are also other imperative forms. You can check this: http://www.placedauphine.net/random/PolishGrammar.pdf. There is a chapter regarding imperative. If you want more extensive treatment of the subject, you can watch this video: https://www.youtube.com/watch?v=sGSsExKYT6Y.
You give (Present Simple) - Ty dajesz/Wy dajecie (Here I have to use the imperfective verb "dawać" because "dać" as a perfective verb doesn't have present form, thus "(Ty) dasz/(Wy) dacie" would mean "You will give")
Give! - (Ty) daj!/(Wy) dajcie! (imperative)
I must give it to him - Muszę mu to dać (infinitive)
Czy możesz dać mi więcej ryżu? Can you give me more rice? (also you can actually add "mamo" - that's vocative, if that's really addressed to your mother, probably at the beginning or the end of the sentence.
Czy mogę prosić o więcej ryżu? Can I ask for more rice? (Perfect for situations when you're not sure whether you should address someone formally or informally - you change the subject of the sentence to yourself!)
Oh, I meant that it would be 'enough' with 'ty', but for 'pan/pani' you would need to rephrase the sentence anyway.
Actually, "Poproszę więcej ryżu" seems like the most natural option. If we keep closer to "give" from this example, the imperative construction for 3rd person is "Niech pan/pani da mi więcej ryżu", and then of course it's better to add 'proszę'.
Thanks, I know that. 'mi' is the short form of 'mnie' as explained here https://pl.wiktionary.org/wiki/Aneks:J%C4%99zyk_polski_-_zaimki#Zaimki_rzeczowne for example. But it is only mentioned that short form can't be used at the beginning and at the end of the sentence.
More explanation is here http://www.jezykowedylematy.pl/2011/07/mnie-czy-mi-kiedy-ktora-forma/ and it says that short form can't be used when the accent falls on that word. Ok, 'give me more rice' kind of falls into this category. But then what about perfectly legit phrases like 'miło mi (cię poznać)'?
Good question that I had before too. Now I am not a native speaker to be able to give a perfect explanation, but I will answer from what I have learned from the distinction of "lubię cię" vs "lubię ciebie." Lubię cię is the normal way of saying it, the other one "lubię CIEBIE" can mean in a context of "I like YOU (not him)" or something like that. So daj mnie więcej ryżu would work similarly(?). Can a native speaker confirm this or say what I explained is wrong if it is? So... To answer your question of accepting it or not as an acceptable answer, that's I guess up to the Duolingo team to allow you to write sentences that are "specific but uncommon." Sorry if I explained anything wrong here. Again I am not a native speaker.