1. As long as you have bounty, they will try to arrest you. You need to remove you bounty one way or another. If you don't want to pay your bounty, or spend time in jail, check the console commands for how to remove it. How they "talk" to you when you pass by, is determined by what you have done it the game so far. The game is an RPG, and the world changes around you by your actions.
2. You could remove side quests yes. But the main story is not possible to ruin (if it is a NPC you can't kill, because it affects an important quest, they will just kneel for a couple of seconds, standing up again with full HP. But smaller quests become unavailable when you kill a quest giver, or an NPC that is required in that quest.
3. My horse has died in battle. Ran into some giants, and boom, dead. It also got killed while fighting some mountain lions. But atm I got the Dark Brotherhood horse, and it seems to be unkillable.
4. Well, when you own a house, you get the key, you get the rights to it etc. Entering a "stolen" house at night will still result in bounty (if not open), and you will not for example be able to get married and move into that house (marriage is actually possible in skyrim). The items you put in the chests etc might become marked as stolen goods when you retrieve them, not sure about that part.
5. Vital quest items can't be dropped. If you try to drop them it says "quest items can't be dropped". Just try
Hope that is what you where looking for