Joined the Companions and was wondering if any of the containers are safe so I can store some gear?

I have not found any, and trying to confirm through users online has reaffirmed this. Seems the mages guild is the one of the only places where you get a specific room with safe containers (except the barrels I think), besides the player owned homes.

I store dragon bones and scales in one of the drawers on the quarters they gave you, I don't know how long I stored it there but I think maybe 3 weeks or so.

Couldn't say

The easiest container test for me is to save a separate file, place something in the container, then save over the new file again and reload it. The items you put in a container you are unsure of will disappear immediately upon reloading the game again so you will know for sure if its safe or not.