Thornmouths primary abilities stem from knowledge itself, the incarnation of all knowledge being the Mindflame.
Time Shifting - From context it appears to mean the ability to manipulate time. This is reflected in our rare, innate incantation that is The Night of Endless Learning. When this incatation is utilized nighttime hours are extended to permit more reading to be achieved.
Philosomancy - These two are concepts not concrete.
Philo, denoting a liking for a specified thing, and mancy, divination by a specified means. From this context it can be inferred that this is divination by by use of favorite objects.
Edit: Philo, referring to something concerning exisitence, as in Philosphy and mancy as in magic. So the magic of existence.
OR classification for literary and mental magiqs.
Second Mind - Maybe use of the mindflame as an extension of the mind. That's my best guess for this one.
Astral Thinking - Astral Projection, Out of body experiances, Bells cited traveling to the lighthouse in her dreams last night.
Tome Kindling - Capablity of "reading" books in third person. Travelling into the book and observing/interacting with the story.
Peering Arts - All other divination methods.
Those are my best guesses.