I say "some" juice because asking for "one glass of juice" sounds needlessly formal and asking just for "juice" sounds blunt and rude. Plus, when you ask for "some juice" it means you are asking for an undetermined amount of juice.
Idk. It's just how I ask for some juice or milk or water or nearly any request with family or friends. If i were at a restaurant i would ask for a glass of X....
The way "can i get" comes across depends mostly on the tone of voice, and the setting.
If we're talking about formal English grammar then yeah, "can i get" is considered "improper". The thing I'd always hear from teachers back in school (in the US) was "I don't know, can you?". This is because technically "can" should refer to your own capability to do something, not whether you have permission from someone else.
Outside of the classroom, though, "may i have" feels overly formal, and at least where I live you mostly hear "can i get" or "can i have".
You'll occasionally hear someone take issue with saying 'get' instead of "have", but at this point in history that's usually someone being pedantic or classist (to be frank).
How polite can this sentence be considered? If we were to translate it quite literally to either "juice, please." or "Can I get some juice?", I'd consider it to not be very polite. Therefore, can this be considered the Japanese equivalent of "May I get some juice, please?", "Could I please get the juice?" or something similar? Or is there a more polite version of this?
(This question is about the usage of kudasai in general. Can it be considered very polite, or not?)