Star

A star was a ball of gas composed of hydrogen and helium. Stars existed throughout the universe and often were orbited by planets. Perihelion was when a planet got closest to its star. (HOMEVID: The Zero Imperative)

By the pattern of the stars in a sky, one could determine one's time zone. (TV: Heaven Sent) After the TARDIS landed on Skaro, the First Doctor hoped to fix their position by the stars since he and his companions had left their previous location too quickly to get any fix. (TV: The Daleks)

According to the Twelfth Doctor, stars were "born" every day. Rusty cited this as proof that life prevailed. (TV: Into the Dalek)

Composition
In the pre-universe, stars were doughnut-shaped. (PROSE: Millennial Rites) When the universe was rationalised they became spherical. (TV: The End of the World, 42, Amy's Choice, The Rings of Akhaten) In the after-universe, the stars were spherical, but usually green. (COMIC: The Stockbridge Child)

Stars gave off a wide range of radiation, including ultraviolet light, visible light and more dangerous radiation. (PROSE: The Sons of the Crab)

Stars of sufficiently large size would destroy themselves in a supernova. (TV: The Pandorica Opens)

Manipulation
In general, only more advanced species were capable of manipulating or using stars.

The Time Lords were capable of controlling stars to their own ends. They used stellar manipulators like the Hand of Omega to control stars. (TV: Remembrance of the Daleks) The Tenth Doctor said they invented black holes. (TV: The Satan Pit) They used the black holes to power their time travel. (TV: The Three Doctors, The Deadly Assassin)

The Great Old Ones could be returned to their bodies by the positions of the stars. Unfortunately for them, the constant expansion of the universe meant the stars would never return to their proper positions. (PROSE: White Darkness)

The early Chronovore fed on stars. (PROSE: The Dark Path)

The Osiran GodEngine was capable of destroying a star. (PROSE: GodEngine)

Fate
Ashildr watched the stars die at the end of the universe, a sight she found beautiful. The Twelfth Doctor disagreed, believing it to be sound, though Ashildr suggested that both were right. (TV: Hell Bent)

Other references
The First Doctor claimed that his truth, which he searched for, was in the stars. (TV: The Daleks)

The Twelfth Doctor, claiming to have kept count, confirmed to Rusty that the Daleks had destroyed "millions and millions" stars. Rusty, noting that new stars were born despite this, voiced the view that life prevailed. (TV: Into the Dalek)

The reality bomb caused the destruction of all reality, making the stars seem to "go out". (TV: Turn Left, Journey's End) The total event collapse, the destruction of the universe, caused every star to supernova. (TV: The Pandorica Opens) The stars went out when the Great Intelligence invaded the Doctor's time stream to turn all of his victories into defeats; this was witnessed by Madame Vastra on Trenzalore. (TV: The Name of the Doctor)

130 years after rendering Jack Harkness a mortal by cutting him off from the Time Vortex, John Hart realised that something was wrong as stars appeared closer than they should have. Jack revealed to John that, since he was a fixed point in time, John had endangered the universe by allowing him to die, the moving stars being a result of time and space contracting. Ultimately, the alternate timeline John had created was negated when Jack perished. (AUDIO: The Death of Captain Jack)

Torajii was a living star. (TV: 42)

The Gryphon was made of artificial stars. (COMIC: In the Stars)