Hello Zajigirl! Only Daniel will be able to delete a district but editing a title should be possible for you unless it's been more than 24 hours since you created the section. Try logging out and in again and see if the "Edit Title" link on the page in the right corner shows up. If that doesn't work, could you stick the URL and correction here for me please? I'll change it for you then :).
Short answer: Keep it in "Restaurants & Eating", and change the type to "Café, Light Food, Soups, Tea".
Cafes are a bit tricky - they may go into "Restaurants & Eating" as well is in "Nightlife & Entertainment".
In Restaurants & Eating, there is a type "Café, Light Food, Soups, Tea".
In Nightlife & Entertainment, there is a type "Café".
I would base the decision to put it in "Restaurants & Eating" or "Nightlife & Entertainment" on how people use the place. Is it a place where people come together in the evening to have a drink? Or is it rather used during the day for a light snack? In most cases (including your example), I believe "Café, Light Food, Soups, Tea" in "Restaurants & Eating" is the best fit. You can change the type on the listing page if you like.
I think I also need a listing changed. I put a cafe under restaurants but think it should be under Nightlife and Entertainment. The cafe in question sells lots of different coffees and teas but only two or three food items. Although it might still be fine under restaurants. What do you think?