Yes, in principle it can be installed, provided the tower has a 5.25-inch drive bay and a free SATA port. The device is an internal optical drive with a SATA connection, and internal ODD options are provided for the HP EliteDesk 8 TWR G1i depending on the configuration.
The answer is no. Only drives in which the disc is placed on a turntable can be operated vertically. Vertical operation is not possible with devices where you have to insert the disc. I hope I have helped, even if the answer is not the one I was hoping for.
I have not bought the adapter myself and operate the drive internally (I am absolutely satisfied with the product, fair price). I looked at the adapter, and according to its description, the drive should also be able to be operated externally.
Let's put it this way: Very probably, no drivers are needed because the API is standard, but without guarantee. And from then on, e.g. Roxio Toast. Or whatever.
I myself have tried several LGs on a 2009 with Sierra and 2-3 versions before.
The product comes with CyberLink MediaSuite 10 for BluRay (OEM version) and includes the PowerDVD 12 player, which can also play Blu-ray and Blu-ray 3D.