Usually "zu" means "to" or "too." But in this case it's part of a very specific phrase — "zu Hause" means "at home". It's the sister of "nach Hause," which you use if you're going home (Ich gehe nach Hause). Best just to memorize those two, since literal translations don't make any sense.
I agree, this word is becoming more and more ambiguous every time it pops up in this subject.
The -e ending is the old dative-case ending.
It dropped off from most words but was kept in some fixed expressions including nach Hause and zu Hause. (But we say e.g. in einem Haus and not usually in einem Hause.)
Such idioms often preserve old grammar and vocabulary that is otherwise not in use.
Actually I would disagree (for the English translation). I don't know if it's grammatically correct but in a conversation it is perfectly likely and acceptable to hear 'is someone at home?' Yesterday, for example, a family member was coordinating a move and organising a van to go to the house, they needed someone to be there to accept delivery and indeed said 'is someone at home?' It was quite a specific question, it was emphasising the importance that someone should be there, else the plan would go to pot. I bellieve that 'someone' CAN be used in this case and it is emphatic.
Some-/any- in questions is subject to colloquial variation but negatives definitely prefer any-. "Did we get some/any?" "No, we didn't get any". Positives prefer some- "Yes, we got some" Any in a question may imply need versus want for some: "Did we get some? (Because it would be nice if we did)" "Did we get any? (Because it is important that we did)" But even with that, emphasis can allow any/some to be interchangable in that context.