According to the novel, Serenity, which is excellent as is the Visial Companion, the funeral is held at Haven. The book says "their graves". I don't know if it is where they are actually buried. I would guess: yes, it is their burial place since they are back on Haven. I'm sure they would not have tied Book's body to the ship and they would have Wash's body and could have brought Mr. Universe's body back too.

The ship repairs take place on Persephone/Eavesdown Docks, because, "it wasn't the best repair shop in the 'verse, but it was the closest, and there was only so far they'd get with only one thruster.

Hope this helps.