Unfortunately, the answer to most of your questions is "It depends". Some good infographics that will help are:
http://statpics.blogspot.com/2014/12...dimension.html shows river flow in North America. It's one of those hand-wavy "average" things, of course.
http://www.ngdc.noaa.gov/mgg/global/...histogram.html shows some Earth altitude summaries based on the ETOPO1 DEM.
#1: effectively 0 (most estuaries) to 900 meters (a sheer granite outcrop like El Capitan in Yosemite) over the course of a kilometer is possible. Generally, the weaker the material, the lower the terrain relief.
#2: 0 to 50 km, depending on season. Some rivers disappear completely at certain times of the year. The Amazon can get to 50km wide or more at its mouth during the rainy season. The closest persistent feature labeled "river" to where I am rarely gets more than 15m wide when it's raining, which would barely qualify as "river" in a lot of places.
#3: The highest and lowest depths are largely a function of the strength of rocks, especially at depth. The strength of rocks is critically dependent on how much water is in them (contrast topography on Venus with that of Earth, for example: http://www.seafriends.org.nz/oceano/ocean28.gif ).
#4: This goes back to strength of rocks. 4 billion years ago, tectonic plates were much smaller due to both hotter underlying rocks and to less fractionation of continental crust from crustal basalts.
#5: The amount of erosion is proportional to the amount of water present, local slope, and material type. More water=more erosion; steeper=faster erosion; softer materials=faster erosion. As clouds move over a mountain range, they lose water (orographic precipitation). As clouds move farther from the source of moisture that formed them, they lose water. Note that local vegetation can act as a source of moisture: it's called the rainforest not just because it receives external moisture, but also because it makes its own rain!
There is a constant interplay of mountain building vs. erosion. An orogeny (mountain building episode) occurs when local conditions cause uplift that's faster than erosion such as at an active convergent plate boundary or hotspot. The newly-uplifted elements are typically sediment-covered and tend to erode at a high rate. As the topography is eroded flatter and/or more resistant rocks emerge, erosion slows. Eventually, in the absence of uplift, everything would be planed down to sea level (check out the life cycle of a coral atoll from volcano to seamount).