"It can travel anywhere in Time and Space..... and it's mine."
-The Doctor describing his TARDIS.
The TARDIS is the Doctor's way of transportation through the space-time continuum. TARDIS stands for "Time And Relative Dimension In Space". Therefor it is another dimension from a non-linear subjective point of view. The TARDIS runs on the Eye of Harmony, which is a black hole ripped out of space and put in stasis, therefor generating infinite energy (gradually, only. Over time). The TARDIS can Time Travel through the Time Vortex, an always-existing plane of reality which under-laps the Omniverse as we know it, full of immense power that if absorbed or come in contact in any way, it would have devastating consequences.
The TARDIS, or any other, should have a chameleon circuit which scans the surroundings of when the TARDIS lands within 30 Gallifreyan kilometers, chooses the most inconspicuous item in that radius, and shape-shifts into it all within a nanosecond of landing, no matter how big or small the object is. Unfortunately, since the Doctor's TARDIS's chameleon circuit blew, his TARDIS's form was permanently stuck as a Police Telephone Box.
The TARDIS is a Type-40 Series 3 Capsule, ancient in Time-Lord terms, an old old model that was the only one the Doctor could steal. If it were given back to the Gallifreyans (If they still existed) it would most likely become a relic, a museum item.
The TARDIS was designed to have 6 pilots flying it, one for navigation, destination, shields and so on. Since the Doctor went rogue, he was the only one to pilot it and has been piloting it alone ever since (This excludes his companions helping him, e.g River Song, Donna Noble, Martha Jones etc.).
Time Travel - The whole purpose of the TARDIS was to Time Travel, so it does.
Time Manipulation - The TARDIS exploding destroyed all of history, jumbling it up therefor manipulating the Timeline.
Matter Manipulation - The TARDIS has infinite energy and can be put to good use, therefor can manipulate space and matter in general.
Energy Manipulation - Ditto.
Near-Indestructibility - The TARDIS shields are ridiculously tanky, having survived a super-nova, escaped the sheer force of a black hole (The Gallifreyans created Black Holes) and avoided damage at the heart of a dense galaxy exploding.
Near-Impenetrable - The TARDIS shields also protect from teleportation, beaming, matter conversion, abd even phasing/transcending techniques. This wastes a lot of energy and can drain the power flow.
Jelly-Baby Dispenser Edit
The only source of food besides The Fridge (Currently) is the TARDIS, but it can ONLY dispense Jelly Babies.
(I've had permission from Demo for this).