Shayde

Shayde was a Gallifreyan construct, placed on the Doctor's TARDIS against the Doctor's will and without his knowledge. In time, the Doctor's fifth self — and later his eighth incarnation — found a way to work with Shayde, despite the fact that, ultimately, Shayde was beholden to Rassilon and the High Council.

As a construct, rather than a fully organic being, Shayde had the ability to both emulate and actually join with other beings. Thus, his adventures with the Doctor occurred with him in one of three main identities. The "default", unitary Shayde that the Doctor's fifth self exclusively knew was followed by a Shayde who was pretending to be a new incarnation of the Doctor, who then joined with Fey Truscott-Sade to become "Feyde".

The "default" Shayde
Shayde had his origins in the Matrix, where the minds of the physically dead Time Lords who resided there created him. He was a servant of Rassilon. An earlier, female construct, the Pariah preceded Shayde. The Pariah was another construct of Rassilon, but he tried to destroy her when she developed free will and rebelled against him, massacring a few thousand Time Lords. The Pariah survived the ensuing conflict, landing in 1879 Arkansas, where she merged with a human and created the first of the Threshold. (DWM: Wormwood)

The Doctor first met Shayde as he appeared in order to help him defeat Melanicus, at first covertly but then, as the Time Lords increased his power levels and he was able to manifest himself, directly. (DWM: The Tides of Time)

He aided the Fifth Doctor against another force, a mutated Gallifreyan creature called a rovie that had infiltrated the Doctor's TARDIS and was trying to kill the Doctor and his companions Peri and Erimem. (BFA: No Place Like Home)

Shayde encountered the Doctor again when he was in his eighth incarnation and was dying due to the events of a recent adventure. (DWM: Tooth and Claw) His companions at the time, Izzy and Fey, had taken him back to Gallifrey, where he was cured and his mind placed within the Matrix to recover. While in the Matrix, an attempt was made on the Doctor's life by a secret Time Lord sect known as the Elysians, which Shayde prevented. The assassination attempt was part of a plot by Overseer Luther, an insane Time Lord who wanted to rewrite Gallifrey's history and set himself up as a god. The Doctor thwarted Luther by short-circuiting his watchtower (a gigantic TARDIS), but apparently at the cost of his life. As Izzy and Fey watched, the Doctor regenerated into a new incarnation. (DWM: The Final Chapter)

As the Doctor
The Doctor's "regeneration" was a ruse. The Doctor had realised that Fey was under external control when she had managed to pilot the TARDIS even though the TARDIS manual was in Gallifreyan script, which she did not understand. Just before the Doctor prepared to sacrifice himself, Shayde offered to take his place and fake a regeneration. This way, the group that was controlling Fey - the Threshold, now a mercenary organisation that the Doctor had tangled with before - would seize the opportunity to bring a newly regenerated and thus weaker Doctor to them. Both disguised with personal chameleon circuits, Shayde would hold their attention while the Doctor sabotaged the Threshold's operations.

The TARDIS landed in Wormwood, a Threshold stronghold which resembled a Wild West town on the Moon. When Shayde and the Doctor revealed themselves to the Threshold, Shayde had to contend with the Pariah, who wanted to take revenge, not just on Gallifrey but the whole universe. Shayde was unable to defeat the Pariah on his own and so crushed the globe forming his head. Fey merged with the dying Shayde and together killed the Pariah and defeated the Threshold. The shared being, dubbed "Feyde" by the Doctor, although both of them retained their own consciousness, decided to leave and deal with what had just happened to them. (DWM: Wormwood)

As Feyde
Fey returned to her own time period, the 1940s, where as an agent of the British government, she spent two years fighting the Nazis. Shayde would not allow her to use their powers to kill Adolf Hitler, as this would change history, this has caused the two to form a love/hate relationship, complimenting each other whilst resenting aspects of their flaws. In 1941, she received a sub-ether summons from the Doctor - Izzy had been kidnapped, and the Doctor needed Shayde's abilities to track her whereabouts. (DWM: Me and My Shadow) Together, they succeeded in recovering Izzy. "Feyde" returned to World War II. (DWM: Oblivion)

Powers
Among Shayde's many powers were the abilities to travel through space and time and, via a sleek pistol that he carried, fire deadly self-generated psychic bullets. He could also make himself invisible to security systems, phase through solid objects, and, given enough data, accurately track people through time and space. Additionally, he could, at least in his original form, remove his spherical "head" and store things in his "body" via the resulting, apparently dimensionally transcendental, gap. (BFA: No Place Like Home)