(1) SL didn't 'find bits of old songs'. He wrote an original one based on a story.
(2) He fitted the song to a tune which may have been quite old (unlikely) or quite new(ish).
(3) No, this does not constitute 'a traditional song'.
(4) The White Hare (in this form) wasn't revived because it wasn't lost. It didn't exist.
(5) The tune is never likely to be considered trad (despite its unknown authorship) because its structure is not trad,
(6) Neither Smoothops nor the BBC are due for any congratulations whatsoever.