Hello,
In order to be able to enable and display labels for features, the labels must first be enabled for the shapefile in ArcMap. Once the labels are displayed as desired, save the layer to a Layer File and then open that .lyr file in ArcGIS Explorer. This also applies to the second question. In ArcMap, set the symbology to Categories > Unique Values and then save the .lyr file once the features are being displayed as desired. Using that symbology renderer, you will be able to specify different colors and symbols for different values in the same layer.
You will only need to create a single .lyr file once both the labels and symbology are set in ArcMap. This functionality is unavailable in ArcGIS Explorer because this software is mainly used for read-only applications and does not allow for any data manipulation.
I hope this information helps.
Thank you.