Then "it all happened via random mutation" is likewise a fundamentally worthless statement for two reasons:
a) We know from the fact that humans practice ID, that it is a potentially viable explanation for any given characteristic, especially those we have not directly observed to occur;
and b) if Design is not falsifiable as an explanation, then neither is the alternate claim that random mutation accounts for any and all characteristics that we can observe.
Sure it can. There should not be a completely random pattern of mutations in organisms if mutation and natural selection is the mechanism of speciation. If mutation and natural selection is the mechanism, you would expect to see the same mutations in different species. If you observed completely different mutations in different species, then mutation and natural selection is falsified. (Note the converse is not true, ie. if you observe the same mutations in different species it is not necessarily the case that mutation and natural selection must be true. It does lend support to that model, however.)