I am trying to save selected features into a new shapefile using QGIS 10.2. The new file does not contain the aliases for the field names.
Is there a way to maintain the aliases in new files?
You can retrieve the field aliases, when you save the style of your original layer to .qml and then load it to your new layer:
Open the layer properties: At the bottom of the window, there is a Style button (next to Help).
Save from orginal:
Properties -> Style (dropdown) -> Save Style -> QGIS Layer Style File
Load to new layer:
Properties -> Style (dropdown) -> Load Style ...
Of course, this will transfer also all other styles and settings of the original layer.