I assume you mean that you want the tracks connecting to the vias from the BGA pads to be 4mil and the tracks from the vias to the rest of the circuit to be 5mils. If that is the case, there's no way for you to write rules to accomplish that completely automatically - there are too many variables if you are autorouting.
To get close, you could establish a room that contains only the BGA footprint. Then you could write a rule for 4 mil tracks in that room and on the top layer. You might have to manually adjust some top layer escapes that don't go to vias because they would cross the logical limits set by the rule.
The teardropping of selected vias can't be done completely automatically. You would do that after routing is completed. You would use Find Similar Objects to select the vias matching those within your footprint. Then you would use Deselect Outside to deselect everything outside the footprint. Once that is done, and you have just the footprint vias selected, you use Tools>Teardrops to add the teardrops to just the selected vias.