The Plot Armor ability more seems to fit into causality, but if I'm wrong please correct me. Also, please tell me if there's anything wrong in general.
I'll get to the Rassilon, Omega, Toymaker, and Misc stuff in the next post.
Time Lords' powers (natural): Healing (Can share Regenerationn energy with other beings, healing their injuries or ailments, and decreasing their age), Limited
Reactive Evolution (Within their Regenerationn cycle they are capable of gaining new attributes. The Doctor described his newly regrown hand as a "fighting hand" after having it severed in combat),
Precognition (Time Lords can naturally see if events in time are fixed or can be manipulated. Foresaw a day where the Daleks would have killed all life in the universe)
Time Lords' powers (technology): Biological Manipulation (Can force and control the Regenerationn of Time Lords),
Acausality (Their Transduction Barrier locks them in an "Inner Time" which is temporally cut off from the regular flow of time),
Magic and
Law Manipulation (Were described as having "squeezed" out magic),
Conceptual Manipulation (Can place beings on an abstract plane of existence with Shift. Conceptual bombs are capable of destroying concepts, such as the concept of TARDISes),
Existence Erasure (De-Mat technology and Time Bombs can directly erase opponents from time),
Power Nullification (Capable of nullifying Time Lord Regenerationn with many of their weapons),
Time Stop (Can create slices of frozen time),
BFR (Can extract opponents from space and/or time),
Sealing (Can seal off entire time lines. Their deaths closed off the universes access to parallel ones)
The Doctor: Precognition (Time Lords can naturally see if events in time are fixed or can be manipulated),
Resistance to
Mind Manipulation,
Telepathy,
Extrasensory Perception (Could keep his name from various beings with these abilities. Can withstand mind probes, which are potent enough to boil a human's skull, has a "complete mental block" powerful enough to keep out the his Cyberman personallity, which was far more intelligence than himself) and
Biological Manipulation,
Causality Manipulation and
Probability Manipulation (It was stated that causality loops around him and that the "odds collapse" in his presence)
^ Prep: Acausality
TARDIS: Resistance to
Radiation Manipulation (Immune to a Magno-Grab with Shield Oscillators),
Air Manipulation,
Sound Manipulation, Can detect Conceptual Beings,
Technological Manipulation (Can generate virtually any machine in the Universe),
Mathematics Manipulation (Can use Block Transfer Mathematics in order to manipulate Space and Time),
Matter Manipulation (Can reconstruct particles),
Creation (Is able to create virtually any item. Can make a seemingly limitless amount of "echoes" of its console room),
BFR and
Time Stop (Was able to freeze and send Gallifrey into a parallel pocket universe. The TARDIS froze its "heart" in time after being destroyed),
Dimensional Travel (With great difficulty, it can travel to bubble universes outside space-time, however, it is unable to travel to parallel universes),
Conceptual Manipulation (Type 2, Above the Time Lords. Has all the powers of the guardians of time who can manipulate the six concepts they represent)
The Master: Time Stop (Froze planets in time),
Resistance to
Perception Manipulation (Was able to see through The Doctor's perception filter, and even claimed that it didn't work entirely) and
Mind Manipulation (Resisted a Time Lord weapon that attacks the mind),
Illusion Creation,
Power Nullification (Can negate Time Lord Regenerationn with Staser and Laser Screwdriver),
Status Effect Inducement (Picking up the Master's umbrella results in paralysis),
Pain Manipulation with telepathy,
Size Manipulation and
Durability Bypassing with Tissue Compression Eliminator,
Age Manipulation with Laser Screwdriver (Contains Lazarus technology, which allows him to increase or reverse a person's age)
Edit: It turns out the Magno-Grab doesn't use Magnetism, rather a bubble of radiation.