1) Back when I was a SEN I used the E lounge despite my flight departing from D, mostly to see off friends departing from E. We were not connecting so couldn't claim to be using E as an arrivals lounge. This was in July.
2) If you have priority, which I'm guessing you do because you're talking about lounges, I think a quick visit to the city and walking up/down Bahnhoffstrasse are very doable. Of course, what you do on that walk might not fit in. But I've frequently done it for watch hunts on connections.