Can an undirected, random process create so much diversity?
Well evolution is actually neither undirected nor random.
Direction is created by selection pressure.
Ever hear of parallel evolution? Look it up. It pretty much disproves your premise.
Favorable traits are selected for - there is nothing random about that. That is why we can measure aspects of the environment and predict what kinds of animals and plants should be found there. If it were random it would not be so predictable.
There is some randomness associated with mutation events but even mutation is not completely random. Certain loci are more susceptible to mutation than others.