What is the statue with the 4-toed foot, and how and when did it crumble?
The statue was of Taweret, the hippo-headed goddess of childbirth for the Egyptians. Jacob lives inside a chamber below her right foot. She crumbled in 1867 when the Black Rock, riding a huge tidal wave, was forced into her. What we don't know is why she guarded the island, whether she has anything to do with the fertility issues (not like there were tons of women on that island having tons of babies pre-1867), or why the Egyptian themese are so prevalent (have also seen heiroglyphs in several places, a relief of Anubis with Smokey, etc.)

Does Smokey truly possess dead bodies? Hasn't it appeared in forms other than persons or animals who have died or been dead on the island?
It would appear he does not "possess." Just "appear as." It does appear that everyone or thing he has appeared as has been quite possibly dead, but not necessarily dead on the island. Usually, it is some one or thing from a person's memories.

How did Ben get a cancerous tumor so aggressive that it could be inoperable in one more week on an island that heals everyone else of diseases, including cancer?
This was probably a part of Ben's faith being tested. His bitterness over this led to him being succeptible to MIB's manipulations. His angry questioning of Jacob before he stabbed him was devoid of him realizing that while Jacob might have caused or failed to prevent the cancer, he also quite possibly provided the healing hands of Dr. Jack Shephard to make it better.

Why are there bodies still chained up in the Black Rock? This would assume everyone died when the ship crashed on (or was transported to) the island. Either that, or it assumes that those who survived didn't care to release their prisoners from their chains if they were alive, and didn't care to bury them if they were dead. Why not?
We now know that Richard and other slaves were prisoners held below, and Whitfield killed all of them but Richard out of fear that if they were released, they would overpower the ship's officers.

Is Claire alive, dead, or somewhere in-between?
Claire almost certainly died in the mercenary attack on her barracks house, got infected and claimed, and now is "sick." She mirrors Rousseau as the island's resident crazy outdoorsy chick.

What happened to the Black Rock after it set sail in 1845? How did it end up so far inland?
We know that Jacob called it to the island, and a huge tidal wave washed it a mile into the jungle. What we don't know is: What secrets does the ship's journal contain? Why have they never been made public? How did it fall into the hands of pirates, or get off the island in the first place? Why was Torvard Hanso selling it at auction, and why did Widmore buy it?

What is the purpose of the ring of ash surrounding the cabin?
We know that ash keeps Smokey out, as it did when Bram protected himself (momentarily) with a circle of it around himself. We don't know WHY, though. We also don't know why a cabin belonging to Jacob would need to be ashed-off from the MIB. They've visited each other plenty of times before. Did the ash perhaps keep Jacob trapped inside, such as when Locke heard someone say "Help me"?

Was Ethan involved in the Purge, too?
We never saw him, but he would have been around 15 at the time, and was born to Dharma parents with the last name Goodspeed. We know he rejected this name and chose the last name Rom and joined the Hostiles, like Ben. 

Widmore says he knows WHAT Ben is. Does this have anything to do with how Ben survived his gunshot wounds as a kid, and Richard said he would be forever changed?
Quite possibly. Mostly, though, we know more about the procedure Ben underwent in the Temple Pool that healed his wounds and saved him, but did not work with Sayid, probably because of the discoloration, probably because Jacob was dead.