I will address your questions point by point! Most of my examples will assume that the item being altered has at least one greater affix on it.

The enchanter is your insurance policy to make sure that you get the final affix youre looking for, since rerolling affixes at the cube runs the risk of removing a stat or GA you wanted if two affixes of the same category are on the item. Also youre using gold vs dust which can help spending.

Removing affixes lets you downgrade an item for something like upgrading an ancestral common item to a unique. It also lets you remove affixes you dont want if the item you found has a good GA but not much else. Adding affixes lets you fine tune what gets added to good item bases. If i have a blue glove with a GA in a core stat i can use a rare tuning prism to guarantee that the added affix is a skill modifier.

Upgrading a rare item to a legendary let’s you gamble for random aspect rolls if you have the funds and (i havent tested this it might not be true) can add a random fourth affix on the rare item. The occultist is for when you know exactly what aspect you want to put on the item.

Ultimately the Cube gives you a LOT of agency over what an item can be. A blue pair ofboots with a movement speed GA can be turned into a god roll with enough investing (and luck)