Natural gene mutation really is a random event. Polymerases, which make new strands of DNA and RNA, are not perfectly accurate molecules. RNA polymerase has an error rate of approximately 1/10^3bp, and DNA polymerase has an error rate of approximately 1/10^6 bp. It is this minute error rate that allows natural selection to drive evolution.
As for your second question asking whether or not it is possible to cause a specific mutation (i think you mean phenotype) to appear, the answer would be, at the time, no. this is because directed mutation is not an available technique at the time. Using transposable elements, one can cause mutations to occur, but they are largely random, or confined to specific areas of the genome. However, this methodology is obsolete. We can cause specific phenotypes to show in an organism by directly adding or removing pieces of DNA- so there is no need to mutate a cell in order to cause a specific phenotype to appear.
The technique of inducing mutation is a commonly used protocol in reverse genetics- where one seeks to find the gene responsible for an attribute by mutating segments of DNA until the attribute is no longer observed.
Also, one can cause specific TYPES of mutations (U>A or C>G) to occur, because it is possible to predict what mutation a base pair will undergo if you subject it to UV light, mutagens, etc.
Hope this was helpful