The list of outputs to present after a simulation is available in the Outputs tab in the simulation settings window, and you can choose to include as many or as few outputs as you wish. Note however, for probabilistic simulations specifically, that including many outputs could exhaust your memory and also slow simulations down.
When a new simulation is run, the old results are removed. When the new results are available all the plots and tables will update to show the latest results.
If you want to keep the results when a new simulation starts - for instance in order to compare old results with new - right click the result and choose Create archive. The archive will remain and a new folder with the latest results will be added to the list.
If you want to save the simulation results to file, either save the project as an assessment or right-click the result and choose Export archive.