Just as the question suggests, if I have Wingfoot attached to a Ranger hero, who then has their text box blanked by the condition attachment Shadow of Fear (from Flight from Moria), does the attachment remain or fall off?

Similarly, Burning Brand on a non-lore hero who had the appropriate song attaches to be able to place Burning Brand, but later loses the Song attachment.

It'll stay on. The restriction only matters when you're paying for/attaching the card.

Interesting. In other FFG games like Game of Thrones, it falls off.

Yeah, this breaks from Thrones. The exact ruling here is in the FAQ:

" The “Attach to...” rules text on an attachment is only a play restriction, and is not taken into account after the card is already attached. "

Excellent. thanks for the clarification.