It depends on how you define 'random.' What you describe are events of known cause and consequences, and even though they influence evolution, they are not causative elements of evolution.
No single element in any stochastic process is sole "cause" of the emergent properties.
The fitness function acts upon random inputs.
But consider mutations due to background radiation....these are random inputs in the process.
Randomness whether it exists or not is not a causative factor, and neither is the more accurate fractal variation in the occurrences and outcomes of mutations in evolution. Physical Laws are the determining factors in the outcomes through the environment and organic chemistry.
Physical laws are of course operative.
But nonetheless, random inputs play a role in stochastic
processes, which yield non-random emergent properties.
These might be useful to you....
Stochastic process - Wikipedia
Transition between Stochastic Evolution and Deterministic Evolution in the Presence of Selection: General Theory and Application to Virology
Creationists are wont to claim evolution is impossible because a purely
random process cannot generate such complexity of life. But facing
the existence of random inputs doesn't give them any ammunition.
It's the combination of random change & the fitness function which
give rise to evolution.
If you claim that the inputs are not random, then whence do they
originate? Divine guidance? Nah, I don't see that as useful.