Say I found a nice house whose owner was sadly dead (Hlaalo Manor) and I decided to move in - would any items I place in the house stay there? Is it safe to leave stuff in such places?

i'd avoid using storage just in case it's respawning(check uesp for detail)
if that's the house with the dead guy lying on the floor you can store items in his corpse safely, and bottomless, but may bug out when filled with 3 months worth of treasure.
can always and perfectly safely dump stuff on the floor/shelves too

Containers shouldn't respawn, but you'd best check this to make sure. Everything you place in the house by dropping it on the floor will definitely stay.

Thanks!

The containers in the house should be safe from respawning, but there's another issue. MW has a serious issue with stolen items. Some of the crates and barrels are "owned", and regardless of whether the owner is alive or dead, anything you place in them will be considered "stolen" if removed later. Worse, all of that particular item in the game will be flagged as stolen for the rest of the game, even if you no longer have the "stolen" ones.

The corpse, oddly enough, doesn't have "ownership" issues, and makes a fine container, although it does tend to distract guests' attentions from the other decor......