Would an Inquisitor have their own astropath? How many astropaths are there, actually - one per planet, dozens, hundreds..?
BTW. Any ideas as to where an Inquisitor could live? Would they have some sort of big headquarters etc.?
Would it be fitting with the setting, if my game had a heretic who wasn't a psyker, but who managed to summon daemons through rituals etc.? And, to whom, the daemons would be "whispering" etc. even before the summoning?
Again, there's no hard and fast rule whether an inquisitor would have an astropath, or live in a particular place. Some inquisitors have massive retinues with multiple astropaths, others have a few henchmen with no astropaths. But being inquisitors, if they need an astropath, they can just requisition one from the nearest Adeptus Astra Telepathicus station. I'd imagine that there would be more astropaths on a planet the more important the planet is, and if it's like, a major Imperial Navy shipyard, there'll be hundreds. Fluffwise there are Inquisitorial fortresses scattered across the Imperium's worlds, where resources like intel, inquisitorial stormtroopers, etc are available, so an inquisitor might very well choose to live there. Alternatively, he might attach himself to a crusade's command echelons to police the purity in the imperial forces there. Or he might rove around in his personal ship, or hire out a rogue trader's, or so on. It's all up to the inquisitor's personal tastes; they're inquisitors, they can do whatever they bloody well want.
Rituals, with some form of warp-tainted artifact of sort. Daemons can be bound to items, or warp powers might bleed and corrupt items - worlds that have been sucked into the warp often have everything on them tainted, for instance. Again, there's no real set of guidelines. Just imagine how modern day demonology in them movies, and apply the necessary 40k window dressing.