Inserting a token will increase your pet's stats by several points, but I'm not certain exactly how much.

You need to have an item with the word "boot" in it to protect yourself from the vending machine. :P Not sure if other items will also work, but I'm pretty sure that works for sure.

Oh sorry, I forgot to specify in your inventory, not on your HA.

I should also mention, though, that kicking the machine also has a chance of decreasing your pets' stats, just to let you know.