"[Evolution is] a theory that says that life evolved due to random chance and not anything else.
Do you really think that is true?"
More accurately it says that it's random chance or genetic mutation that is then directed by natural selection.
"Something approaching randomness may produce a genetic adaptation in an individual (a cosmic ray hitting a gene), but whether or not that adaptation is beneficial in an environment and whether the individual will have a genetic advantage over those without the adaptation is not random."
It's not random at the low level where you consider if a specific adatpation was beneficial in a specific case. However the theory proposes that proper adaptations hapening at the proper times where they produce a greater tendency to survive is random.
You also have to question the origin of phenomenon we express as the laws of physics. Is the way the universe works by design, or is it mere random chance that gravity works?
If you have to focus in on a theory very closely for it to make sense, you need to question that theory much more carefully.
"Moreover, do you deny that random events shape the genetic heritage of an individual?"
I do not deny that events that appear random shape the genetic heritage of an individual. I cannot prove that they are random, but they do appear to be random.
However, you cannot argue from the particular to the general. Doing so is a logical fallacy. If observing that there appears to be the result of random acts, you cannot extrapolate from that the there is not a design that incorporates those random events along with some guidance as part of a larger plan. An example of such would be the intelligent design of the natural laws which direct natural selection.
You also cannot take an instance where there appears to be a consistent and logical plan being followed and say that plan doesn't happen to be one of many possiblitites and only random chance resulted in it's existence.
Neither randomness or intelligent design are exclusive, nor are they provable causes for an observed event.
"And if an individuals genetic heritage is determined by something other than random events and the application of physical and chemical laws to whatever adaptation the random events cause, can you tell us which parts of that heritage are caused by that something other?"
Nope. Welcome to the realm of theories. It's the realm of things we don't know, and it's much larger than the realm of things we do know.
This is why we must teach theories as theories in schools, and stop with indoctrination where we only teach one possible theory to explain something.
A strict religious school that refuses to teach evolution is failing to teach students to think critically and teach them how to learn. The same goes for a public school that refuses to teach ID.