1. I don't think anything you leave on the ground or on top of furniture will dissapear. I am on my 1st playthrough at around 375 hours and I still use it as one of my main "homes". The garden and alchemy shelves have respawned ONE time and nothing I've had on the ground (quite a bit) has ever dissapeared.
2. I don't know but I don't think so. I didn't even know you could have "your dog" do anything besides follow or wait or leave you.
Nothing disappears that you've dropped. I left the Staff Of Magnus, one of J'zargo's scrolls, and a Wisp Wrapping in the display cases there. Everything you take that's there initially will respawn though. Even the soul gems on the shelves and the cheese on the table.