1. If you\'re peddling enough to accelerate (or even maintain your speed against the wind) then something is exerting a forward force on the bike. The friction with the road is the only candidate. So the friction force on the bike points forward and on the road points backward. (Remember that as you pedal, the tire starts to turn, pushing backwards on the road.) If you\'re braking, the force points the opposite way. If you\'re coasting, the frictional force on the tires is very small.
2. You\'re right that the type of tire, and its inflation, can change the contact area. You\'d guess that big contact areas would allow more friction. On the other hand, the smaller the contact area, the more pressure (upward force per area) the road exerts on the tire within that area, since the pressure times the area has to equal the supported weight. In other words the tire and the road are more tightly pressed together when the contact is small. It turns out that these two effects approximately cancel, and the maximum friction force is more or less given by a material-dependent friction coefficient times the \"normal\" force (up-down, here) between the surfaces.
Sometimes we need a more accurate description of the friction. People who really care about friction (eg, drag racers) maximize the contact area in order to maximize the adhesiveness of the tire to the road. Especially in uneven conditions, the large contact from a slightly squishy tire does a better job of keeping contact somewhere, rather than occasionally bouncing out of contact.
Car and bike tires have grooves in them, which might seem strange since it reduces the contact area. Their main purpose is to improve performance when the road is wet. The water goes into the grooves and does not form a slippery film between the tire and the road. The improvement of wet-road performance outweighs the degradation in dry-road conditions.
Mike W. , Jon T, and Inga K.
(published on 02/28/09)