It means that he reaffirms that he intends to do what is right, to the extent ("as") God grants ("gives") him the capacity to understand ("see") what is, in fact, right. (Of course, he could not do what is right if God did not grant him the understanding of what is, in fact, right.)

since

Here it means 'while' or 'when' or similar to that.

here "as" = "how"