The image you provided is exactly Perlin's turbulence function (fractalsum(1-abs(noise(n,pos))) rather than the simpler fractal sum(noise(n,pos))) where n is the current octave number and pos is the input position to sample. Musgrave's RidgedMultifractal adds only an additional term that is more along the lines of fractalsum((1-abs(noise(n,pos))*(1-abs(noise(n-1,pos)))). That extra term makes for much broader basins and rougher mountain areas.

The image you provided is most likely based on either a cubic interpolation or a quintic interpolation function ( http://mrl.nyu.edu/~perlin/noise/ for the quintic-based noise function and the justification for it over the basic cubic). The interpolant is the basis of the noise function; the character of the result depends to a large extent on the basic table used for random numbers and the interpolant between samples in that table. Some folks use an arbitrary image as the input to the noise function, while others dispense with the noise table entirely and generate the noise values directly from the sample coordinates themselves.

Distorting the inputs before doing the inputs is described by Musgrave as "domain distortion" and a search on that term might be fruitful.

The incise flow algorithm is a very simple one: a direction map is calculated for each point on the surface that shows the local "down" in altitude. Then that map is traversed and each pixel sends a counter up the gradient, adding one to each sample on the flow map. At the end of this operation, every point on the surface then contains a value that represents the number of cells that would contribute to the flow at that point. Applying a logarithm operator and a threshold operator to the flow map will generate "rivers" across the map.

Antialiasing is also pretty simple: just sample the noise function multiple times at each displayed pixel, then use the average of those samples as your noise value. If you'd rather do coverage sampling, then the percentage of samples above sea level would represent your land opacity over ocean at that point. The same algorithms used by ray tracers and a lot of GPU renderers can be used here as well.