Sure! but it is a little funny and pointless ... what if there is no answer? In what situations would you want to say it? On the phone, beside your sleeping partner, on the train beside a snoring passenger? Maybe 'are you quite awake', 'are you wide awake' are more likely questions. There are no common synonyms that come to mind, but for someone slow to respond we would say 'come on, wake up!' 'get cracking!'

It's fine. Here are some other ways to say the same thing: 1) Are you awake yet? 2) Are you up (yet)? 3) Are you (still) sleeping? 4) Are you there?