Ground connections and symbols in schematics: should they be separate or connected?
All the ground symbols must be connected together.  The exact routing of the connections does not matter.

In the circuit you show, the negative terminal of the battery IS NOT connected to ground.  It is connected to the "ring" terminal of the input jack, and the sleeve of the jack is connected to ground.  This arreangement means that the circuit is turned on when a plug is inserted in the input jack, and automatically turned off when the plug is removed, so an actual power switch is not required.