As I understand it
What are the names of the ??? pieces above? If they don't exist, why not?
The interim step in rum making is called 'Wash', which unlike beer or wine isn't sold separately. I don't know exactly why, but I suspect it's because it doesn't taste good. The same is true of just about every spirit, including brandy and whiskey, you don't want to drink the first stage product.
To be a little bit technical, the first stage of whiskey making is an ale, or very similar to an ale. However, the fermented product that is made in whiskey making isn't a product you'd bottle and drink, again because it doesn't taste very good. Whiskey makers use different yeasts and encourage bacterial growth to add character to the end product after it's distilled, I'm told it's sour, unpleasant and very strong.
Brandy is made from wine (not always grapes, you have apple brandy, apricot brandy and others), however what makes a good table wine doesn't make good brandy. Special wine is produced for brandy that isn't bottled for consumption because it's acidic and not sweet.
You have to ferment sugarcane molasses (which is just concentrated boiled sugarcane juice) to distill into rum, so I'm not sure fermented molasses has any other name.
The second question was already asked and answered here, and it's simply 'distilled mead'.
Ferment sugar you get ???. Distill that and you get rum.
Distilled Sugar Cane is also called Cachaça. Rum is made with fermented molasses, while Cachaça is made from fermented (fresh) cane sugar.
According to here, the interim product you are looking for is called Wine Cane, though it looks like it's more commonly called Sugar Cane Wine:
Once the sugarcane juice has been filtered, yeast is added for the conversion of the sugar into alcohol. During fermentation, the yeast converts sugars into alcohol in less than 24 hours, producing a beverage of approximately lighter ABV also known as wine cane.
In the Canary Islands (Spanish), you can buy Ron Miel. In Madeira (Portuguese), you can buy Ron Mel. Both names translate as Honey Rum, but they are made by fermenting sugar cane (mel de cana in Portuguese).
The attached photograph was taken in a sugar cane museum in Calheta, Madeira.
Fermented sugar gives you all alcohol. Boiling grain gives off sugars. Rums get made from cane sugars and you get vodka that is nothing more than fermented sugar water.
Brewers yeast is a micro organism that takes sugar of varying sort consumes it and produces alcohol and co2 as a by product.
