Yep, the Tein Flex kit includes everything you need - already pre-assembled - and ready to install on your car. I believe that the Flex also comes pre-set to the recommended ride height. The HAs, on the other hand, had to be assembled by the end user, at least the ones that reused the stock upper mounts.
As for what a pillowball upper mount is - I assume you installed your shocks yourself? Remember threading the top of the shaft through a couple of rubber donuts that located it on the upper mount? A "pillowball" upper mount replaces those two rubber bushings with a metal spherical bearing, which allows for a more rigid shaft mount, and also minimizes side loads on the shock shaft itself from the upper mount. Basically it's a little louder, transmits a little more ride harshness (those OEM rubber donuts are there to improve NVH isolation at the sacrifice of damper precision), but also allows the shock to do it's job more effectively because it's basically rigidly mounted to the frame of the car, so it experiences no side loads or isolation.
Another benefit to typical "pillowball" upper mounts is that they tend to take up a lot less of the shaft's length, which increases your damper travel range. In the case of the Flex, the rear upper mounts are also elongated back into the trunk cavity, which further increases damper travel. Make sense?
Depending on how late this year you pick them up, you're welcome to come and see the installation process on my car, since I plan to be installing the very same suspension (although probably with stiffer springs) on my car at the end of this season.
Iain