As edladner said, for ship range you can use tech research to improve range. You can also go into the ship designer and equip a ship with more range modules.
Your maximum fleet size is determined by logistics, which is shown in the top right of the fleet display (bottom left corner of galaxy view). To increase logistics, this is done through research.
To mine Durantium and Elerium, build a starbase (using a constructor) nearby the resource. You must then send an additional constructor to the starbase, click manage (bottom left of galaxy view), then build a mining ring (top right pane on manage screen).
Durantium and Elerium are useable for weapons at the end of the tech tree.
Hope that helps!