If I was to leave a sword next to a standing stone or in the middle of a field, how long would it take for the cell to reset and the sword to disappear?

I haven`t specifically tested, but it`s probably 3 days. If not that then try 10 and if not that try 30.

It will definitely be gone after 30 days.

Does anyone know for sure? I've heard they NEVER reset.

I think it's different for different items... arrows seem to stick around longer than swords do.

On the road from Whiterun to Windhelm, there's a corner where baddies occasionally appear. Over the 339 game days I've played, I've probably killed a dozen of them and all their swords and shields are still there!

By the bridge near the mill,I can't remember the name of the mill right now,there are several of those places in my game where swords tend to remain where they were when I killed the enemy,usually in mid air.
They mostly come from Assassins I think.

But for the OP's question most swords should dissapear after just a few game days.
Other things like Alchemy ingredients can take up to 14 days,if you stay out of the area.
Ore veins take up to 30 days if you cleared the area and I think 14 days if you didn't clear the area.