You don't need to use は with temporal nouns (今日, 昨日, 去年, 来週, などなど). When you use it it means that you're contrasting something, so 今日は京都に行きます would be like "(Tomorrow I'm going to Nara/I'm not going to Kyoto tomorrow, but) today I'm going to Kyoto." 今日京都に行きます just means you're going to Kyoto today. 明日京都に行きません means "I'm not going to Kyoto tomorrow."
To ask if someone didn't eat, you could say もう食べましたか. I'm sure お腹が空いていませんか, お腹が空いていますか, まだ食べていませんか, and もう食べていますか (I believe) would be fine, too. It depends on just what you want to say, though. もう食べましたか is the most straightforward.