To me, it appears that there is a partial blockage. It allows things to go down except when there is a large volume of water, such as when someone is doing a load of wash, or emptying a bathtub, then, because of the volume it can't all go down fast enough, and it backs up at the lowest point - your apartment.
The alternatives to this are that the pipes weren't sized properly, and they just can't handle the volume of all of the fixtures, and it just backs up.
The gurgles could be that the vents are not designed properly, or are plugged up.
One of the pros will eventually critique my thoughts!