Any kind of process which results in an error of replication.
how can we ensure there are no deleterious effects (mutations are generally extremely deleterious),
Since the copied sequence is extraneous, mutations are not likely to be deleterious. The original sequence might not bear the same load of mutations.
... what determines a favorable direction
very little, if anything
and what target is there for a sequence to hit upon?
a fitness selection which is not determined ahead of time.
Do you see how these words "don't get us there" and are, at best, wishful thinking?
No.
Well, what does this mean, "the differential expression of genes" and what is the control mechanism?
The expression of genes is controlled by other molecules, usually proteins which bind to short sequences of DNA up- or down-stream from the protein coding region, and which affect the timing and concentration of protein production. Also, these control elements determine which protein product out of number of possibilities is produced.
You are again speculating. You surmise that differential gene expression results in differential phenotype, and while it would now seem logical, it is not established.
This is elementary material, well established in the literature, available for perusal by anyone with an interest.