I killed Drela at his cottage (Drela's Cottage) just southwest of labyrinthian

Can I use the house as my own? Meaning, the chest at the foot of the bed won't regenerate and delete my stuff, will it?

Will the food and ingredients respawn after a certain amount of time if i take them?

No, almost all containers not in a player-owned house respawn in about a week.

If it works anything like oblivion, your stuff is not safe. If it works anything like Morrowind, you'll be fine. I wish I could be more helpful than that. One rough test is that you could try to sleep in the bed. If the bed still says owned, well you can imagine the containers probably are too so you won't be safe.

If you can sleep there, you'll probably be fine to put some stuff in the containers, but you'll want to test it out for a few (game) days anyway.

It tells you in one of the loading screens that if your putting your stuff in a chest you do not own it may not be there when you go for it later. So I wouldn't do it.

What about the chest where your stuff was held while you went to the party?

I'd assume that one is safe. Bethesda wouldn't risk you losing all that stuff. We won't be able to know for sure until we can check it in the Creation Kit though.

As for any other container in the world, stuff respawns after about a week unless it's in a player owned house.

If you take items from any surface in the game will they respawn? Have not took anything yet and I am wondering...