Have you already eaten lunch?

Have you accomplished anything?
何か成果はありましたか？

"Have you already been to the new bar around the corner?" "Yeah, that's the spot."
「あの角の新しいバーもう行ったか？」「行ったよ。あそこ最高だよな」

Have you already eaten lunch?
お昼はもう食べた？

Have you already given notice?
もう届けをだした？

Have you already had lunch yet?
もうお昼食べた？ 

Have you already paid the invoice?
その請求書の支払いをもうしましたか？

"Have you always been interested in English?" "My father got me into it."
「昔から英語に興味があったの？」「父の影響でね」

Have you and Sylvia discussed this thoroughly?
君とシルヴィアはこのことを徹底的に話し合ったの？

Have you applied for the job?
その仕事に応募しましたか？