Yes, you could call them the city-wide winner.

Mount Everest, it just hadn't been discovered yet.

If you say "to church", you mean to any church. It doesn't matter which church you go to. If you say "to THE church", you mean a specific church. You have probably already said something about which church you would like to go to.

You could, but it would be more likely that you would say the dorm is "a stone's throw" from the cafeteria. "A stone's throw" means not very far away. I keep a glass of water on my bedside table so it is 'within easy reach' during the night. Literally, it takes very little effort to reach out to the glass. The glass would be within reach (but not 'easy reach') if I placed it on the desk across the room from the bed because I could still get it, but I would have to walk to the desk first. It can mean something which is not physical. Healthy food is within easy reach (because fruit and vegetables are cheap and you can buy them anywhere): it is not physically close, but it is easily achieved.

'kicking in' means starting. The new rules kick in on Thursday. The new rules start/take effect on Thursday. The heating hasn't kicked in yet. The heating has not yet started to warm the place. The drugs will kick in any minute. The drug effects will be felt very soon.

Yes.

im Suden means 'in the south' sudlich von means 'south of' London is im Suden (in the south) Germany is sudlich von Denmark (south of Denmark), but that doesn't mean it is in the south of Europe, it's still in the north.

You can just say 'I need to BREAK this vicious cycle'. Of your 2, I would say 'BREAK OUT' because a cycle is something that you are in, so you can't really break 'through' it.