Answer to Question 1
From the headwaters to mouth, there is usually an increase in discharge and channel size. Gradient decreases, as does channel roughness (due to a decrease in sediment particle size). In order to accommodate the growing discharge, channel size increases downstream as well, and so does flow velocity (despite decreasing gradient).
Answer to Question 2
Sufficiently strong water flow can dislodge particles from the channel and lift them into the moving water. A stream can also erode bedrock with by the particles it carries, acting as abrasives or drills into the streambed.