Pokemon-go – directly battle the friends

It appears to be tied to the pokémon itself, rather than anything relating to what gym it's in. I have a Slowbro with "Battles won: 2", and that message immediately appears in any gym I put it in. There doesn't seem to be any way to view this number in the summary page, however.

To receive the defender awards, you must have at least one Pokémon in an allied gym.

To collect the rewards for having a Pokémon at a gym, you have to go to the shop while at least one Pokémon of yours is still defending at an allied gym. Thus it is best to capture as many gyms as possible (up to 10) and then collect before any get taken down. To get to the shop, from the home screen tap the Pokéball icon, then tap "Shop". Then inside the shop, there is a button in the top right where you can collect rewards for having Pokémon in a gym. Note that you can only collect once per 21 hours.

Also, as pointed out by Virusbomb, "the rewards for defending a gym are 10 Pokecoins (which can also be bought with real money and are used to buy in game items) and 500 stardust. You can get a max of 100 coins and 5000 stardust every 21 hours with Pokemon in 10 different gyms."