Is it possible to manage the placement of the telescope mirror in a specific location through the operator, or do we have to randomly view the data reflected to the telescope ?
Yes, Hubble is actively controlled from the ground.
Examples include monitoring and adjusting the spacecraft’s subsystems (e.g., power, thermal, data management, pointing control, etc.), flight software development, sustaining engineering of the control center hardware and software, and systems administration of the network and ground system components.
Images taken with Hubble are carefully planned. The telescope must be pointed in the right direction and hold this attitude for a prolonged time.
Compare for example the Hubble Deep Fields.
The first Deep Field, the Hubble Deep Field North (HDF-N), was observed over 10 consecutive days during Christmas 1995. The resulting image consisted of 342 separate exposures, with a total exposure time of more than 100 hours, compared with typical Hubble exposures of a few hours
The telescope does hold the programmed attitude on its own. A good overview over the way the Hubble holds attitude is given here:
Basically, the desired attitude for an image is carefully calculated on the ground. The attitude is then sent up to the telescope, as well as the instruction for what images to take and how long. The telescope then controls itself, rotates to the programmed attitude and takes the pre-programmed shots. It has fail-safes to ensure that it never points at the sun, which could damage the telescope.