Lots of information there, Tornado! Just a few things that might not be quite accurate, though:
it was suggested at the end of the episode where Tennant's Doctor is seperated from Rose for good, that it was actually the TARDIS who "accidentally" places them aboard, as the next companion just materialised as the cliffhanger for the end of the season. The TARDIS seems to react to his emotions and does seem to act to protect him. I got the impression it beamed the next person aboard to prevent him moping over Rose.
I never got any suggestion of that at all. While the TARDIS is "alive", as the Doctor has said, and she's telepathic - as is he - there's never been any suggestion that she 'interferes' in his life in any way (unless you assume that Rose 'inhaling' the Time Vortex in
Parting of the Ways was somehow aided by the TARDIS). Actually, the appearance of Donna in the TARDIS is fully explained in the 2006 Christmas episode,
The Runaway Bride.
He can choose to look like anything when he regenerates.
Actually, it's never been suggested that the Doctor can. There is some indication that Time Lords could - Romana, for example, chose to regenerate and she 'tested out' several bodies before choosing the one she preferred (way back in the Fourth Doctor era). However, the Doctor's regenerations have all been sudden and/or violent, and that gives him no choice. Remember, at the end of
Parting of the Ways he says to Rose "This process is a bit dodgy. You never know what you're gonna get."
He officially has thirteen lives, not ten. Twelve regenerations, meaning thirteen bodies. But the BBC has been dropping hints that this may not remain canon - Gallifrey's destroyed, they've said, so who knows what would be the case now?
There definitely are plenty of similarities between Superman and the Doctor. Sara compiled
this table on her LJ a while back, based mostly on the Ninth Doctor. Nine and Rose... my favourite combination
He seems to attract blondes and redheads.
Don't forget Sarah-Jane! Or Romana I, or Leela. And, of course, Jack.

Not to mention the new companion, Martha.
When he does meet up with old companions there is often a hint of them treating him as an former ex.
Well, that was really only Sarah-Jane, as she's the only past companion he's bumped into in recent years. In the old series, there was never any hint of anything more than friendship with companions, until the Eighth Doctor, who kissed Grace Holloway several times - but she never travelled with him. The novels associated with the Eighth Doctor (not aimed at a teenage market, unlike those for the Ninth and Tenth) hint at a bit more sexuality - companions making passes at him and even kissing him, with mostly passivity on his part, apart from one very strong hint that he may have slept with one of them (Berniece Summerfield, known as Benny).
The Master - he and another woman turned up in some of the earlier series as surviving TIMELORDS.
Well, don't forget that before the Ninth Doctor's era Gallifrey still existed. There was still an entire race of Time Lords, and we met a number of them, not just the Master and the Rani. Romana, Iris Wildethyme and many others - some episodes were even set on Gallifrey, including one where the Doctor was elected President of the Council. It's only since the Time War that the Time Lords have ceased to exist - though rumours abound that at least one may have survived.
Cybermen seem to hate everything that isn't mechanical and they aren't exactly happy with the Daleks but as the Daleks are usually more powerful they have often attempted to team up with them against the Doctor.
Um... no. The recent season finale (
Army of Ghosts and
Doomsday) is the first time Daleks and Cybermen have ever been used in the same story, so the first 'encounter' between the two. And, really, they fought each other. There wasn't any sense that they were teaming up to defeat their common enemy. In this recent era, the new Cybermen (manufactured by John Lumic) use the cry
Delete! but the original Cybermen, from a planet called Mondas, used to say
Eradicate! As for the Daleks, the Doctor's reminders that he destroyed them refers to the Time War - past encounters with the Daleks don't involve this bit of psychology on his part. As to whether he could do it again, the Fourth Doctor was sent by the Time Lords to Skaros (the Daleks' home planet) to destroy the Kaleds before the Dalek race was formed, and he couldn't do it (
Genesis of the Daleks). Nor could the Ninth Doctor destroy the Daleks a second time (
Parting of the Ways), though the Tenth Doctor did send them into the Void, and lost Rose in the process (
Doomsday).
Oh, and there were two or three versions of K9 - Sarah-Jane got one, Romana II apparently absconded with another and I think Leela may have had one as well. And, of course, he built Sarah another one to replace the original K9 when he got killed saving them all.
The Doctor's family... Well, the First Doctor travelled with a teenage girl called Susan who called him Grandfather. There's discussion around the possibility that she may not have been biologically related to him at all, though much of this comes from old-schoolers who hate the idea that the Doctor might have ever had sex or procreated

In
Fear Her he told Rose that he was a dad once. I think we may find out more about that in subsequent episodes.
Oh, and the sonic screwdriver... the universal
deus ex machina device.

The Fifth Doctor lost his and it was gone for many years, on the basis that the writers felt it had just become too much of a handy plot device. There is a
hilarious exchange between Jack and the Ninth Doctor over the sonic screwdriver in
The Doctor Dances:
JACK
Okay. This can function as a sonic blaster, a sonic cannon, and a triple-enfolded sonic disrupter. Doc, what you got?
[The Doctor takes the sonic screwdriver out of his pocket, but Jack is not looking as he is too busy brandishing his sonic device at the gas-mask people]
DOCTOR
A sonic, er... oh, never mind.
JACK
What?
DOCTOR
It's sonic, okay? Let's leave it at that.
JACK
Disrupter? Cannon? What?
DOCTOR
It's sonic! Totally sonic! I am sonic-ed up!
JACK
A sonic what?!
DOCTOR
Screwdriver!
JACK
Who has a sonic screwdriver?
DOCTOR
I do!
JACK
Who looks at a screwdriver and thinks "oohoo, this could be a little more sonic"?
DOCTOR [indignantly]
What, you've never been bored? Never had a long night? Never had a lot of cabinets to put up?
(Edited a little - in the midst of the 'willy-waving contest' Rose is trying to figure a way out of their situation)
Anyway, the thing with Doctor Who is that there's more than forty years of TV history, not to mention all the novels and audios (which aren't strictly canon). So - like Superman history, in a way - some of the canon can be contradictory. One thing I do like about New Who is that the writers do make use of classic canon, but do it in such a way that people who loved the old series will recognise the references, but those who came to it new won't realise there are things they're missing. For example, the enemy in the first Ninth Doctor episode, the Autons, are from classic Who. In
Dalek, the Doctor sees a Cyberman head in Van Statten's museum - nothing to notice for a new fan, but a bit of a 'squee' moment for old-schoolers.
Wendy (who adored the Ninth Doctor and now sees the Tenth as a close second)
