It looks like Stake has a decent (Medium lifestyle) condo. Achak has a Low lifestyle in Seattle. Sister Rebecca, being new in town, will need lodging.
I'm not 100% clear what standard procedure would be in this case. I'm guessing we're not being pursued, but there's always a chance that Higher Powers will connect the dots and come after the painting, if it is indeed worth anything. Achak also has a gangland hideout/safehouse in Puyallup for laying low. It's not nice (squatter) but it's secure and he has the relevant gang boss as a contact. It's in the Puyallup Barrens.
I also don't know if the social convention is to stay together until the job is done (i.e. bounties redeemed, booty fenced) or if there's enough history and trust between Stake and Achak to make that unnecessary. I envision there being a trust between them, but perhaps Sister Rebecca feels differently.
Achak would certainly like to clean up. Who knows if the squatter place is going to have water at any given time, and odds are it won't be hot. Plus, it's December, so things aren't exactly balmy outside. I'm also guessing that he and Sister Rebecca would like to attend church in the morning - probably an 8am service, concluding well before the appointed meeting time - but I don't know how picky Sister Rebecca will be about where she worships. Achak is flexible enough that he would accept an invitation from Stake, but perhaps Sister Rebecca would prefer to squat, per her nomadic tendencies.
Achak's favorite food is Indian fry bread, with either sweet or savory toppings. If sweet, he would eat it with soykaf. (Real coffee would be wiz, but he probably thinks that ¥50/cup is an unconscionable luxury.) With savory fry bread, I can imagine him drinking a cola-flavored Slurpee-doo. In my head, he has a sweet tooth. He probably loves NERPS. He also grew up with orks, which probably means that's he's used to bold flavors that would make most of us gag.