Translation:Is this glass half full or half empty?
'czy' is used in questions, when you have an A/B (or more) choice.
'albo' and 'lub' sometimes can also be used in questions, but then it suggests that both A and B may be correct. And frankly, I think that sometimes we may accept them too easily, they are of course a possible interpretation, but sometimes too weird.
And here... well, I'd say that asking such a question, you really want your interlocutor to choose either A or B, not both.
Częścią mowy jest tutaj wyrażenie przyimkowe (Adpositional phrase). Najpierw jest przyimek "do", a potem mamy rzeczownik "połowa" w dopełniaczu (Genitive).
I don't know if you are sarcastic, or genuinely asking? Yes that's the same thing described from different perspective.
I'm a rationalist so I just think of it as 4 ounces of water in an 8 ounce glass.