It feels a bit stupid to ask this, but I have to know.

If you drop items in your houses, they will not disappear - that cell does not respawn (I guess). You can drop ingredients on the floor, books in the bookshelf etc. and they will remain there forever.
I you drop stuff in an Ayleid Ruin or a dungeon, will it disappear? Or is it just the stuff you put in respawning containers that will?

Someone will hopefully correct me if I'm mistaken, but the cells do respawn, including your own houses. However, items dropped by the player have a special status that make them stay even when the cell you dropped them in respawns. This means that if you loot a dead enemy in a ruin and just drops on the floor everything you don't want, those items will stay there (and in your savegame) forever. If you instead put them back into the dead enemy, they will disappear together with the dead enemy when that cell respawns. Now, if you never come back to this cell, it doesn't make a difference because then the cell never respawns .

I've always had issues with player-dropped items disappearing. The first time I bothered actually decorating a player house in-game with my stuff, I came back to the house a game week later and more than half of my stuff was gone. It was a purely un-modded stock player house, too. There were many different types of items on many surfaces, some even in display cases; so while I know bad collision can cause some items to fall through the floor, I find it hard to believe that was the only cause. I've also seen it over and over again since then - not that I'll ever go nuts "decorating" again, but sometimes I'll drop a single item somewhere just to see if it's still there when I go back, and it's usually not. Sometimes I've found the item far under the floor, but most of the time the reference is gone (can't be selected in the console with prid, the reference is really really gone).

In theory, TheNiceOne should be correct. In practice... well, put your stuff in safe containers, if you really want to keep it.

When you drop an item from your inventory, It's a newly created instance of the base form, and it gets a formid starting with 'FF'.

If you just "grab" an existing item and move it around, it retains its original formid. A non-persistent item you moved will get recreated at its editor location when the cell resets, but if you put it into inventory and dropped it again, it becomes a new persistent item and stays put (except for the havok issues of falling through the floor etc.) If it was marked persistent before you grabbed it and changed its position, it's still persistent, so its new location goes in the save.

Does all that make sense?

Thank you! You just resolved one of my redecorating peeves! Now that bloody silver mug that I placed on shelf 3 will stay there!

Also beware if you're running Kuertee's Clean-up mod. That will remove dropped items in cells unless that cell is marked as "safe". I think the usual player homes are marked as safe, but you might want to double-check. I don't think Battlehorn Castle is marked as safe by default, for example.