In the Genres options I see a few entries that are more or less duplicates.
For instance "Be bop", "Bebop" or 6 different entries containing "Ballad(e)" and some that probably don't make any sense to anyone, like "Bolero or Swing" (sic).

I would love to be able to delete (or perhaps alter?) some of these entries to my personal preference.
"Death Metal" eg I will never ever have a use for, so I wouldn't mind it being erased for good.
Is this possible somehow?

When you are in the Song Editor, you can long press on the entry you no longer need when selecting the genre. Then Delete will appear and you can delete the entry.

Go to the "Genres" tab, select the genre that you don't like and choose delete or rename. MobileSheets handles that very clever and conveniently: in case a genre with the new name already exists, it contains all the songs afterwards, both the ones from the already existing genre and the ones from the genre with the changed name.
It might be necessary to make the "Genres" tab visible via Library Settings - Tab Selection and Order. And I recommend to switch  Library Settings - show Number Of Songs to ON. This works similarly also with other groups like Albums, Composers, Selections and so on.