All of those functions return standard data frames. Columns can be extracted by name, predictions(model)$estimate, and all the usual data manipulation functions work out-of-the-box: colnames(), head(), subset(), dplyr::filter(), dplyr::arrange(), etc.
Some of the data columns are not printed by default. You can disable pretty printing and print the full results as a standard data frame using the style argument or by applying as.data.frame() on the object. See examples below.