I would like to purchase a OM-D E-M10 II and I want an extra battery with it. Does it use the same battery as the previous version, the OM-D E-M10?
Does it come with an external battery charger?
Yes, they both use the same battery type. The E-M10 comes with a BLS-5 and the E-M10II comes with a BLS-50. They are equivalent as you can see in Power Supplies for OM-D / PEN series cameras. You can buy replacement batteries for the E-M10 and they'll work for the E-M10II.
Both come with a BCS-5 battery charger that can charge both batteries