I stumbled onto this unusual and visually disturbing site. Yes, I gawked. But it made me wonder what the God-is-omnipotent-and-omniscient crowd think of these sorts of occurrences. Are they evidence of God’s majesty and ability to intelligently design his creatures? Or do they lead believers to think that human are animals who have been cobbled together through natural selection?

I don't understand what these cases have to do with creation vs. evolution. Both sides admit that mutations commonly happen in any population.
External human tails are well documented, and the absorbed-conjoined-twin hand and arm cases are pretty clear.
The frog and cyclops are distinct mal-developments. I'd guess twinned chromosomes, as in the cases of Williams Syndrome and Cerebral Palsy.
The backwards feet puzzle me. But I'll bet it was gestational rather than genetic. An x-ray probably shows the ankles flipped over rather then twisted.
Any embryonic surgeon knows how a nipple-foot can happen. One loose t-cell in the wrong place early in gestation and anything can grow anywhere. If it threatens survival, it causes a miscarriage.
More on human tails:
“To understand this strange phenomenon, we have to appreciate that ID handles scientific evidence the way lawyers handle evidence in legal cases, namely paid to come to a foregone conclusion, no matter how poorly supported. If 1,000 people saw you commit the crime and Joe saw someone else do it, Joe’s testimony is the only one that matters to your defense lawyer. When someone from the 1,000 witnesses appears on the stand, your lawyer tries to make their integrity appear suspect, and to call their competence into question.”
http://www.thedailybeast.com/articles/2014/06/01/the-crazy-way-creationists-try-to-explain-human-tails-without-evolution.html