Best practice is to get your legend as close to what you want as possible before converting.
Start off by giving the layers more readable names -- for example, change the layer name from "InterwarProstitues$Events" to "Prostitutes". Set the symbology how you want it. (This should definitely be done in the layers rather than in the legend, to ensure your map symbols and legend symbols match.)
In the Legend Wizard or the Legend Properties dialog, you have a great deal of control over what is/isn't in the legend, font sizes, styles, shape of polygon, and more. This won't change the symbology (in other words, if your map shows blue and yellow polygons, you can't change them to green and red from the legend properties), but it does change how they look in the legend.
After converting to a graphic, changes to layers won't affect the legend and you can't access the legend properties (since it's no longer considered a "legend" object). You can modify graphic properties (size, shape, deleting things, etc.) -- and per the Esri help page recurvata linked to, "You can further ungroup the legend graphics so the individual elements (the patches, text, and so on) that compose the legend can be edited individually." If you need to change one portion of your legend-graphic, you need to ungroup it.