When ever anyone asks why the companions have their ship on top of their home, it always confuses me. I would get it if they built the place with the boat on the bottom, but why and how on the top?

It's the ship Ysgramor sailed to Tamriel in. After they hauled it all the way to the middle of Skyrim, they just flipped it upside down to use as a roof and built some walls. Using it as the floor would have required digging a very specifically shaped pit in the ground and would have compromised the foundation.