yes
Mainly by water frition the water washes up on the shoreline and takes the sand with it, the after time, the river/streams erode.
Yes, they erode their banks and fill in the channels also.
Well, A river erodes its bed because of erosion of course!. Its all go to do with Hydraulic actions, abrasion, attrition and soluting working in underlying rivers to erode river beds.
Velocity of the water and then the slope of the bed