Halfway through Dirk Gently's Holistic Detective Agency (I'm an episode behind) and ready to share what I think I know so far. POTENTIAL SPOILERS (if I'm right):
In the 1960s, a rich inventor is working on a time machine. He needs a power source, so he builds the power grid under the neighborhood where Todd lives. But he's old and afraid he's going to die before he finishes, so he invents a mind transferal machine; that way, he can put his consciousness in a younger body and continue. In the new body, he falls in love (with who? The mother hasn't been revealed yet. Is this the only thing that doesn't tie in?) and fathers a daughter. He knows his daughter is in danger because people are after his machines, so he hires the bodyguard, Farah. He also hires Dirk Gently to investigate his own death before it happens.
In the end, before he dies, he finished the time machine. He used it to find out how he dies and that his daughter has been kidnapped. He needs to make sure Dirk knows how to find her and save her, but he can't just leave him a note because then the ones who want the machine will find it. So he lays out a bunch of clues that lead to the "death maze" (perfect for H&H!) and the map to where they'll find his daughter at the right time to save her.
I was way off on the First Souls. I thought they would be the first sentient beings who had the ability to transfer into other bodies naturally. That they hired the inventor to build the time machine for them because they wanted to go back to their original bodies. But now I'm disappointed; it seems the First Souls were just a group of thieves who found and stole the mind transferal machine back in the '60s. Now they have a much more nebulous reason to want the time machine. They may not even know what the time machine does, but just want it because the inventor made it and figure it's something useful.
Who summoned the shark that killed the father? I suspect it was the father himself. He knew when the First Souls were coming for him, knew the shark would kill them, and in the chaos his daughter would be able to escape. Why they brought his daughter's consciousness to him in the body of a corgi, I'm not sure. Perhaps it was an extra precaution -- trade the corgi first, then machine, then the daughter's body last?
How do Todd and his sister Amanda figure into this? Their "disease" (gift?) makes (or made, in Todd's case) them sensitive to cosmic phenomena. It makes them able to be in the right place at the right time. I suspect Dirk Gently has the disease/gift too, no one has said so yet, but the CIA mistook his disease for ESP.
Why is Dirk Gently so different from the novels? He seems much less sure of himself than he should be, and increasingly reliant on Todd to do things for him. I think that's what the Rowdy 3 are draining from Dirk every time they encounter him, his disease. I'm not sure if there's an agenda there; I suspect they are something like incubi or vampires who drain the disease from him. They haven't tried it from Todd because his disease is in remission and Amanda's medication blocks them from fully perceiving she has the gift.
The real loose end is, who sent the assassin Bart? I suspect it's the CIA. They may know some of what's going on thanks to their ESP branch and want the machines for themselves. They have a two-pronged approach for stopping Dirk -- one is Bart, sent to kill him, and two is Col. Riggins, who Dirk sees as a father figure. They would prefer Riggins to be able to bring Dirk in as their plan A, which is why they put the assassin on Dirk's trail from so far away (it is taking her forever to drive to where he is!).