Does anybody know if the barrels in there are safe to store things in?

From what I understand, items out in the open and maybe some of the sacks aren't safe. On the UESP discussion page of the arch mages quarters or just the college in general will help you, I remember reading someone's in-depth research of the rooms storage.

It says that all the containers are safe to store in but I'm not sure if they only mean chest and wardrobes or barrels too?

I know for sure the wardrobes and chest are safe. Unfortunately, I haven't checked the barrels yet. I do know however that most of your decorations, which you just put somewhere in the chambers (i.e. on a table, in that little garden, etc.), will get replaced about every time. I only managed to make the Staff of Magnus stay on the "table" fixed at the wall where another staff laid before (although it sometimes moves a few inches ...).

How long is the respawn timer then? Is it 3 or 30 days? Need to check it for myself I guess to find out for sure if I can safely store item/ingredients inside barrels.

The actual cell for the Arch-Mage's Quarter (ie: everything out in the open) resets every ten days. But I've used all the containers for things and they're all totally safe.

Including the barrels?

I don't know for certain, but as a general rule I NEVER store things in barrels or sacks anywhere. They often respawn, and it's nearly impossible to tell which ones do and which ones don't without testing them.

The barrels are safe.

I've never used the arch-mage's quarters before but I often store things in barrels and sacks in my other houses and they've proved to be completely safe.

One of the barrels is not safe. (for me)

I've used the arch-mage quarters as my main living/storing/crafting digs for all my playthroughs.
On my latest, which I started post-1.4, I found that one of the barrels re-set to default, and all the books I had been dumping into it disappeared. That particular barrel re-set at the same time all the other default items, plants, etc., in the quarters. However all the other containers were safe----and I mean all, as I use every barrel and sack in there. The other barrels retained my original contents, even while resetting the ingredients that appear atop the barrels.

The barrel that wasn't safe for me, was in the 3rd group to the right of the alchemy table. It's the one that sticks out into the walkway. Sorry I can't take a pic (ps3).

Ah, thanks man. I will check that barrel out even though all I've stored in that barrel is food So even the sacks are safe? That's good to know

Ok I'm on now.

That barrel sits directly across from the pile of sacks next to the garden.
As you look at the barrel, it has a basket to the left, and a floor sconce and pile of wood to the right.

Yeah, the sacks are important to me, I separate my piles of potions using those sacks....
I wish I could call homier digs like Honeyside my home, but no place beats the storage functionality of the arch-mage quarters, for a craftsperson.