Yes, and part of that circle is called ground. It is just a convention, that we call the more negative potential, ground.
Yes, as long as the battery is connected, it will power the circuit, and energy will be used up. You should put an on - off switch in the wire between the + terminal of the battery and the +9V pad, so you can turn it off when you aren't using it. If the 'circle' is open, then the battery will not get used up. The energy used when the circle is complete, is not all wasted; your circuit requites energy to operate. (A little will usually be wasted in any circuit.)