I would like to know when and where I can safely store items. For instance... can I drop items in any house and be sure that they won't disappear? Do I have to kill the inhabitants of the house first? Can I only drop items in saved houses without risking losing them? Can I drop items in the middle of the woods and come back 100 hours later and find them there?

You can probably drop them on the floor and experience no problems, unless someone picks them up, which could be problematic. Drop them in the house of a companion, so at least you can use them if you can't use them.

I've heard that the game tells you if a chest is unsafe..

they dont 'dissapear', not in the sense that the game just gets rid of them after a set time (not counting things stored in respawning containers)
if you drop something outside, the reason it would be gone on your next visit would be due to an NPC picking it up
and yes you can probably drop something in the woods and have it be safe since the chance of an NPC being there is small
and dropped things in houses you own are the safest, NPCs wont enter there

That's awesome, just like real life.

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they don't disappear but npcs can take them, also certain chests contents respawn after awhile so any items in there will be replaced with its original contents.