Is there current flowing out of an Operational Amplifier output?
Yes, current can flow into and/or out off the output of an op-amp. 

However, an op-amp provides a voltage output. It is the circuit that surrounds the op-amp that dictates what current will flow into/out of the op-amp's output.

To apply hand analysis to your circuit you would assume:


\$V_b = 0\$ (due to op-amp action)
\$V_e = V_c\$ (due to op-amp action)


Apply KCL at the \$V_b\$ and \$V_o\$ nodes. 

You now have 2 equations with 2 unknowns (\$V_o\$ and \$V_c\$).