Learn English – Why is it “argument” instead of “arguement”

It is most likely that "abolition" is the more common form due in large part to its association with the "abolition movement".

France was one of the earlier countries to abolish slavery within its borders, and Société des amis des Noirs was one active group in the movement in France.

The picture on that web page refers to (pardon my French) L'Assemblée Nationale pour L'Abolition de la Traite des Noirs and is dated 1790. Clearly "abolition" was the preferred term in France, and that preference would have transferred to England.

Further, those advocating abolition in England and the US were "abolitionists". It would have been a mouthfull to call them "abolishmentists".

The main reason one might choose "abolishment" over "abolition" (aside from the subtle difference in meaning) is that "abolition" is associated with the movement to end slavery, and thus might be confusing or distracting when used to refer to a different process. But this confusion is not likely in native English speakers, unless the context contributes to the confusion.

It is a simple spelling rule. When full is added to an adjective it becomes -ful with one l. I don't know who invented that rule. Also if full is used as a prefix it becomes ful- as in to fulfill.

Similar in all right and the more informal alright.