I’m chiming in a bit late, but hopefully I can contribute a few good points.
I started a thread on this topic which focused just on the science with a very neutral position towards theological and metaphysical questions:
Long story short, random in the context of mutations and evolution is a statistical measurement (e.g. a Poisson distribution). Perhaps the best way to understand what random means in this context is to define what non-random mutations would look like. In the case of non-random mutations we would expect to see the vast majority of organisms producing the same mutation at a very specific base in response to a specific environmental cue. For example, if we exposed bacteria to antibiotics and they adapted through non-random mutations then we would expect a large portion of the bacteria to produce the same mutation in just one generation. Instead, only 1 out of hundreds of millions produce the needed mutation even though one out of ever 3 or so bacteria produced a mutation somewhere in their genome in a single generation.
“Unguided” would reflect the same view. If an organism is guiding mutations then we would expect the same result as non-random mutations. As to a creator guiding mutations, science is silent on that topic. The best science can do is determine if the observations are consistent with their model of random mutations.
Unplanned gets a bit more complicated. I think it would actually be fair to say that mutations are planned just like one can plan a lottery drawing. Polymerases could be better at preventing mutations, but they aren’t. It seems as though they evolved to produce random mutations. There is also the example of the SOS response in E. coli that causes the expression of a error prone polymerase that increases the random mutation rate. I think it would be entirely fair to call them planned random mutations, in a biological sense. Mutations are actually a function of some proteins involved in genetic systems.
In the scientific view, it is about how well the evidence matches your hypothesis. You can build a model of what random mutations should look like, and then see if the observations match that prediction. Does this mean that mutations are not being guided by a deity? No. All we can do is say that the hypothesis is supported, and tentatively conclude that natural mechanisms are probably the cause. Science doesn’t make any philosophically or metaphysically absolute statements. All conclusions are tentative and open to falsification.