Friction on the front wheel acts mainly sideways. In steady motion, the bearing of the wheel applies an equal and opposite torque to that applied by backward-acting friction, and the bearing applies negligible torque, because I greased it.
The driven wheel has friction acting sideways as well as forward (when you're applying power on the pedals). The forward friction torque minus the chain-applied torque is the angular acceleration of the rear wheel times its angular moment.
If you apply the brakes, the front wheel gets backward friction, as does the rear wheel (but it's prudent to mainly brake with the front wheel).
Depends on the motion of the wheel, the direction of the friction force could be different. Remember the friction force from the ground is the only external force acted on the wheel (Ignore air resistance), 1) If the wheel is accelerating forward, the friction force will be pointing forward. 2) If the wheel is moving forward with a constant velocity, the friction force is zero (if air resistance is included, the friction force will be pointing forward, with the magnitude exactly canceling the air resistance). 3) If the wheel is slowing down,the friction force will be pointing backward.
Also, the external gravity and normal force are irrelevant in this problem.
Friction actually acts backwards, but it is the one which causes forward motion of the wheel. See the diagram for clear understanding: Both the arrows drawn represent an action-reaction pair of forces. The blue arrow(action) is caused due to the force of turning of the wheel(which is actually created by us) onto the ground. Thus there is a reaction force by the irregularities of the ground, which causes the wheel to move front. This is the mechanism. But do remember that the friction acts backwards only...
When the wheel is accelerating, we can imagine the wheel is spinning increasingly. The point (or area) of the wheel that touches the ground actually is inclined to move backward and it gives a forward rolling friction, which is exerted by the ground on the wheel. Of course, the reaction force is exerted by the wheel on the ground, causing the earth moving backward (if we can measure~).