Honom - him Hans - his Apparently we are supposed to use honom ans henne with hos

No, we don't say that.

We never use the definite form after the genitive or possessive pronouns. It would be like saying his the house in English.

And when we're talking about being in a house, we use the preposition i – much like you probably wouldn't say I eat on his house in English.

No, "hos" doesn't work that way.

Yes, that's exactly how it works. "Hos" and "chez" are both prepositions. That's the simple answer to almost all the discussions in this page.

(Of course, when "hos" isn't the possessive of "ho", meaning "trough" :) )

I think you would use "i" instead of "på," and "hus" instead of "hos."

"Hos" means "at...place." "Jag äter åt hos honom" would translate to "I eat at at his house." I find prepositions pretty confusing, too, laregly because there aren't true one to one translations.

Hos is a preposition in and of itself, so it basically has the åt built in. It doesnt translate directly to house, and functions like the french 'chez' (e.g. my place being chez moi)