I used "A Monster with a purpose", "Smiling Certainty", "I am the big bad".

It was never very well thought out, it was meant to be a sword of Damocles curse so you do a certain amount of stress and then you can choose when the stress actually comes into effect. So you slash someone with your sword mysteriously causing no harm until maybe a day or so later when a wound mysteriously opens and they bleed out more thematic than useful.

An Aspect would probably do maybe with a spirit maneuver or a thaumaturgical one. 

Being totally indestructible and healing from damage that's somehow inflicted anyway is part of the basic IoP package.

Does standing in it actually make you indestructible or does it just put an indestructible thing between you and the outside world? If the latter, IoP includes that too.

As for why to stat it, because if you're actually going to use the Doctor in a game he needs to pay for the abilities he has.

The TARDIS is not part of the DFRPG's basic premise.

I'm gonna be honest, this whole plot device thing always kinda makes me groan. It's as if people are so impressed by something fictional that they want it to be awesome in a way that mere mortals cannot quantify. Even if it clearly isn't.

See the problem is scale DFRPG is not scaled for space opera's which Doctor Who is one of. Mythic Speed is 0.1x(to the power off) 1,000,000 the speed of a tardis.  So should the Tardis cost 10 to the millionth power refresh ?

It like asking exactly how many shift of damage the death star blast is doing (and to how many zones)? 
 

Here is the changes I would make to Unlimited Blade Works which would include the powers sponsor (Alya) and agenda from the visual novel. 

Reality Marble (Unlimited Blade Works) [-4]
Description: With the help of a powerful force you can project your soul upon the world.
Sponsor: Alya /Gaia/ the World Spirit   
Agenda: This power is sponsored by the World Spirit in exchange for an Eternity as a spiritual guard dog after death. It's agenda is the protection of the world as a whole no matter the cost on an individual level.

Wait a second... I thought Recovery affected only physical consequences, and spellcasting is mental? Or can you actually take physical consequences (instead of mental stress/consequences) to fuel spellcasting?

Fallout.

TRANSCENDENT SWORDSMANSHIP [-4]
Description: Legends speak of heroes who fought dragons with nothing but sword and mail. These heroes fought creatures with nearly endless power and some of them actually won. Transcendent Swordsmanship channels the power of the heroes of old and uses it to do the impossible with swords.
Sponsor: Transcendent Swordsmanship is sponsored by the spirits, or perhaps the legends, of long-dead heroes.
Agenda: Transcendent Swordsmanship drives its user to destroy evil and to prove his own worth as a hero.
Evocation: Evocations cast with Transcendent Swordsmanship often resemble air or metal evocations, and they almost always emulate sword techniques.
Thaumaturgy: Transcendent Swordsmanship allows its user to cast rituals that tap into the legends of dead heroes, as well as rituals that summon spiritual warriors.
Evothaum: Transcendent Swordsmanship does not grant the ability to use Thaumaturgy with the speed and methods of Evocation.
Extra Benefits: A character with Transcendent Swordsmanship replaces his Conviction skill with his Might skill and his Discipline skill with his Weapons skill for the purposes of spellcasting.
Note: Foci made to boost Transcendent Swordsmanship spells are almost always swords. That being said, there's nothing stopping Transcendent Swordsmanship from becoming Transcendent Axemanship in the hands of a specific character.

From the Sponsored Power Master list.

Assuming your going focused practitioner in a comparatively high refresh game (plenty of refresh) going 5 lore is better than 5 lore and discipline because it can be both.