Are the prepositions ‘at’ and ‘in’ properly used in the sentences?

Are the prepositions ‘at’ and ‘in’ properly used in the sentences?

The tribesmen showed Beatrice, a social scientist, the cottage that would serve as her shelter. She was very excited. Inside the cottage were a small single bed, a study table at one side, and a bathroom. She already discussed with them her intention in staying with them, and they were all willing to help her.