a) While due process will establish only if the charges against the Bishop, the accused, can stand in court, there is reason to be concerned that this process is not as rigorously executed as it should be. "Due process" will establish one of two things - can the charges against the Bishop stand in court or not? Therefore, the correct usage is "whether" and not "if". Also, it is more logical to place restriction "only" on "due process", which will then mean that only due process and nothing else can establish - currently it says that due process will only establish one thing and nothing else. Eliminate.

b) While only due process will establish if the charges against the Bishop, the accused, will stand in court, there is reason to be concerned that this process is not as rigorously executed as it should. Same error in using "if" as in (A). Eliminate.

c) While only due process can establish whether the charges against the Bishop, the accused, will stand in court, there are reason to be concerned that these processes are not being as rigorously executed as it should. Plural verb "are" is incorrectly used for singular subject "reason". Eliminate.

d) While only due process will establish whether the charges against the Bishop, the accused, can stand in court, there is reason to be concerned that this process is not being as rigorously executed as it should. Correct answer. All above errors are rectified and no new errors are introduced.

e) While due process will establish only whether the charges against the Bishop, the accused, can stand in court, there is reason to be concerned that this process is not as rigorously executed as it should be. Same error in the placement of "only" as in (A). Eliminate.