Voltage source absorbing/deliver power?
You are right about the direction of current but not for the simple reason that the sources are opposite. 

The sources could be opposite but current could still flow out of the 1V source (which incidentally you've shown as a current source). It all depends on the value of the the left-hand resistor not the direction of sources.

If the left hand resistor were for instance 0.5 ohms, ask yourself what current would flow in or out-of the 1V source.