I didn't like it

* How did Philip's mother die?

Apparently (judging by what his father said) she really was drowned, and presumably as suicide. The implication seems to be that it's finding out that even Philip knows of her infidelities that pushes her over the edge.

* When his mother died, why did his father not go to London to collect him?

I think his father is consciously portrayed as a very provincial, simple type who would be completely out of place in the big town (which is one reason for the strain in his marriage with Philip's mother, who is portrayed as smart and upwardly mobile). Also, in those days it was quite normal to send children on long train journeys alone, with an adult to collect them at both ends and maybe an instruction to the guard to keep an eye on them. Left with an orphan on their hands, presumably Philip's mother's family simply dispatched him back to the North to his father's care, rather then sending for his father to come and fetch him (and pay double fare to do so).

* Why was his mother depicted as one of the women who was murdered in his book?

The same actress was used to portray the character - probably in order to make the point that Philip feels responsible for his mother's death. This was a story-external casting decision: I don't think that Philip actually wrote his mother into his book in order to murder her, consciously or subconsciously.

* Why was the same actor used to portray Mark Binney/Mark Finney/Raymond?

Presumably again to make some kind of metatextual point: probably that Philip is confusing the imagined sexual predator on his [ex-]wife with the remembered sexual predator from his childhood and the morally compromised character who hires Marlowe, as his alter ego, in his book. I think the casting may be intended to make us question the actual existence of the real-life Finney, whom after all we first see as a line of 'typed' dialogue in Philip's mouth...

* Why does he go back to his ex-wife when he knows he's been ripped off?

The end of "The Singing Detective" seems to confirm, as earlier episodes have started to suggest, that in fact Philip is simply suffering from a high degree of paranoia, apparently a long-running feature of his relationship with Nicola (if she is to be believed). All the Binney/Finney business (generally presented as part of a 'story' that he is narrating to himself in bed) is apparently a jealous fantasy which is exploded when the imagined Nicola from his own subconscious turns round and starts addressing a few home truths (also, presumably, from his own subconscious) to the eavesdropper on the murder scene -- who after all cannot possibly be there in real life, since he is still trapped in his hospital bed.

I think the idea is that there is no Finney, no affair and no rip-off: whether there is in fact any film deal at all or whether this is part of his paranoid suspicions of Nicola's motives for coming to visit him I am not at all clear. But I think the intended message at the end is that his own alter ego abandoning him (in fact 'killing' his creator) equates to Philip abandoning his imaginings and reconciling himself to a second-best life in the real world and a fresh attempt at their rocky marriage. I'm not sure it's the message I'd have liked to take away from the story, but that was the impression I got of the moral that was supposed to be drawn.

But like you, I'm frankly uncertain about a lot of what happened and would have liked the stories to be tied up: it seems the author actively didn't intend to do that.

~~Igenlode, who has been watching the Hollywood adapation

Gather round, lads and lasses, gather round...

your the one whose soooooo slooooooow if you have to ask these questions.

the last one is especially idiotic, and proves you missed the whole point of the series.