The Graak went on his mission to free the Doctor almost as soon as he was created. Starting in the Fourth Doctor's TARDIS, he set about retrieving various objects to get across the Great Divide, after which he would free the Doctor who was in the "time zone" he currently occupied.
Throughout his quest, the Graak was mocked endlessly by the Master, who tried various means to stop him from accomplishing his tasks. The Master even attempted to hypnotise him at least twice.
After completing several of the Master's quests and mental challenges, the Graak finally encountered the seven Doctors trapped at the Heart of the TARDIS.
The Master had sent the Doctors into the time vortex, and they had ended up in the Heart itself. The Graak's energy levels were waning, and the TARDIS was on the brink of destruction.
Making his way through water-filled caves and into the Heart, the Graak used up his remaining life force to materialise the Doctors into the TARDIS, saving the Doctors and the TARDIS at the cost of his own life. (GAME: Destiny of the Doctors)
The Graak displayed no clear personality or emotions of his own, though he followed his purpose according to the Doctors' instructions. During the final battle against the Master he willingly sacrificed his remaining life energy to save the Doctor, showing a capacity for heroism.
Although he floated just above the floor without any visible legs, the Graak was capable of basic movement such as running, jumping and crouching. He was also able to swim, though he did so with a slight degree of clumsiness.
The Graak could pick up and use various items. He could operate the TARDIS console, and access the TARDIS logs, as well as fly the TARDIS between time zones.
The Graak was a translucent, amorphous being with a blob-like body in which glowing orbs floated, two pseudopod-like arms made up of strands of the orbs, and one large orb serving as what the Master called a "potato-like head." Though technically a genderless being, the Graak was generally referred to in the masculine by the Doctor, the Master, and the Brigadier.
The Sixth Doctor's companions from stage plays are difficult to assert with certainty, as different actors played the Doctor in the same play. If a medium is not mentioned, then this incarnation did not have companions who were original to that medium; it does not mean that this Doctor failed to appear in that medium.