Yes, the do have the instincts to build a nest. I watched a recent release build her first drey. She would cut short branched off the oak tree and take them to a fork in the tree. She brought more and more and then they would fall to the ground. She kept trying. They have the instincts but having the skills to successfully build a drey is a learned skill. I guess they learn by trial and error just like us.
Eventually, they build a suitable drey.
Personally, I do feed my outside releases. I always feed my new releases but as far as the others I don't feel it's necessary but I do enjoy the interaction with them so I feed them. I usually stop when the oaks are full of acorns. A squirrel would rather eat acorns from the tree than anything I provide.
A cockatiel box won't work as an outside nest box if it's the type I'm thinking about. Is it the type that PetsMart sells for about $17? If so, they aren't predator proof. A suitable nest box needs a predator guard either inside the box or on the outside around the hole. Predators like raccoons will reach their arms inside the box. In a cockatiel box a predator could reach inside and the squirrel would be trapped inside and within reach of the predator. In a proper nest box the squirrel will be well below the opening and will be protected by an inside shelf that prevents predators from reaching inside. I did use a cockatiel box INSIDE the release cage once when I had 6 squirrels in the RC. I needed extra bedding area in the cage so I used one. Of course, it fell apart pretty fast because it's not designed for outside usage.
Nest boxes are nice for our friends but they aren't necessary. I have 5 in my yard. After spending the weekend cleaning them, I'm sorta on the fence about them. They absolutely must be cleaned at least yearly. 3 of the 4 I cleaned had carpenter ants in them. Once that happens the squirrels will abandon them. The reason I'm on the fence about using them is because I'm not exactly a spring chicken so climbing trees at 60+ will surely result in my breaking my neck at some point.