Mistake. One of the worst things a mid manager can do is draw that line to where the subordinates get the feeling you are too good to hang with them. You don't have to be their buddy, but there is value in mingling with the employees at some point. You don't have to do it every day, but a couple times a week would do wonders for you and you can learn a lot by listening to the people who actually do the work,
Has nothing to do with that. I have a one hour lunch that I'd like to enjoy peace and quiet away from phones, email, etc. Otherwise, I end up getting paperwork, emails, or people approaching me for things. Not only that, I can sit back and play some music, watch tv, etc.