...Are there any safe containers other than in your own houses? Even if I "obtain" a new home by disposing of it's owner, are my possessions safe in this new house?...
Here is a list of safe containers outside of an owned house:
http://www.uesp.net/wiki/Oblivion:Containers#Safe_Containers
My favorite is the hollow log in the Imperial City Market District.
...Even if I "obtain" a new home by disposing of it's owner, are my possessions safe in this new house?...
In this game you generally have to buy a house for it's containers to be safe. Either that or "earn" it by becoming the leader of a guild (but that could questionable for some of the guild master houses, like Arch Mage or Thieves Guild). But in purchased houses the containers are safe. Or Frostcrag and Vile Lair DLC (Battlehorn has some unsafe containers). "Procuring" does not result in safe containers.
... And what about objects that are just dropped on the ground, do they stay there?...
Usually, but sometimes they might fall through the ground and so that's not a great option. It's also messy.
...But please feel free to flame me mercilessly....
We don't do that here... usually