I just copied our responses from discord, because people who are interested in the game might wnat to know the answer to your question:

you don't lose anything but you have to wait another 15 minutes until your hero / heroes are ready to fight again. or of course you can use bread to shorten the cooldown.
It's just a "wasted" fight that could have given you gold and a better rank.
If you attack someone you lose 1 durability on all equipped items though regardless of winning or losing.