1. It doesn't require it to come from a logic_auto, to my knowledge, but that's typically the best place for it.
2. No, it is not. You have to place it.
3. Yes, but things will be screwy. What a logic_auto does is load up everything you want your map to do before it spawns any players whatsoever. For example, changing respawn times (by default it's set to 10 for both teams), saying who is on offense versus who is on defense, getting something to begin moving the moment the map starts, etc.
4. In Hammer, up top (by File, Edit, etc.), there's a dropdown called "Map." Click on it and hit "Entity Report." This will tell you the names of every entity on your map, listed in alphabetical order by type (so all of your trigger_hurts would be grouped together with trigger_multiples below and trigger_gravities above). Use this to find your logic_auto and/or tf_gamerules, then you can either double-click on it or click and go View -> Center 3D Views on Selection.
5. Not to my knowledge.