This varies from which Clan you're training an apprentice in. I'm currently more familiar with the FireClan cats. With the time spent outside of the camp, you just have to be outside of the camp. This is a great time to talk with characters to pass the time and train your apprentice at the same time. The cat that you train with for hunting and fighting varies with which apprentice you get in FireClan. In FireClan, either Willowclaw (the white she-cat left of the medicine den) or Gorsefur (the sitting she-cat to the right of the dens) with teach you how to hunt (Gorsefur if you don't have Cloverpaw as your app and Willowclaw if you DO have Cloverpaw as your app.) Also, in FireClan, either Hawkfeather (the light gray she-cat with white legs) or Willowclaw again will teach you how to fight. In SunClan, Tigerheart (the brown tabby tom guarding the camp enterance) will tell you about how to get outside the clan reputation. Thrushtail (the dusty brown tom with a darker tail next to the dumpster) will teach you how to hunt. Finally, Stonefur (the she-cat at the far right side of the SunClan camp) will teach you how to fight. I hope this helps for now! :)