The talk consists of three main parts. In the first part, I will discuss a trace norm approximation for the interacting Gibbs state of a weakly interacting Bose gas. I will then present computations of physically relevant quantities, including the distribution of the number of particles in the condensate, the joint distribution of particles in different momentum modes, and the full counting statistics of the number of particles in subsets of the torus, all of which use the result for the Gibbs state as a crucial input. Some of the results are expressed in terms of a Bogoliubov version of the Gaussian free field. Finally, I will mention a new upper bound for the free energy of the dilute Bose gas in the thermodynamic limit. These results were obtained in collaborations with Phan Tanh Nam, Marcin Napiorkowski, Blazej Ruba, Giulia Basti, Chiara Boccato, and Serena Cenatiempo.