A1: Just keep following it and it will go to sleep then BAM! bye bye

A2: The best way to complete the mission you are talking about, is to buy a tent, and sleep untill eleven. You can also wait around until eleven, but that is much longer. Once you eleven a.m. rolls around, proceed up the left side of the hill across the river from your house. GO SLOW! There is a group of Sitka that will be beaded down. If you move to fast they will wake up. Find the largest sleeping buck, and DON'T MISS!

A3: In case you are wondering, "sleeping" in the game for a deer is simply laying down. They dont ever actually fall asleep. just shoot when they lie down.

A4: They can't be just laying down. It will tell you Mission Failed. They have to be SLEEPING!