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16a Butt out in green trailer (4-4-3-8)
Looks like it might be 'mind your own business' but I can't see why (or why the use of hyphens).

43a Missile thrown, killing dogs initially surrounding donkey (5,4)
'Smoke bomb' fits.

43a is correct

S MOKE BOMB

killing = bomb, as in a lot of money
dogs = comes after
initially surrounding = s
donkey = moke

Mind-your-own-business is a plant

https://www.rhs.org.uk/weeds/mind-your-own-business

ChrisE, thanks for the plant info - I'd wondered, very briefly, about the hyphens and the 'green trailer', but I had other puzzles to tackle so did nothing!

Thank you, didn't know the plant or moke.

7d Published author thomas draws attention to novel. (3,3,4,5)
P-T, -U-, --R-, F-A-S

20a Recollection of dul, echoing dong (3,3)
-A-, T--
TAT TAT? Can't see it really but why

Sorry but can't see how to edit my post:

20a should read 'Recollection of dull, echoing gong

The first one is a novel by Evelyn Waugh.
PUT OUT (published), (Thomas) MORE, FLAGS (draws attention to)

Dull can be MAT

TAM-TAM is a gong

jono and candledave - thanks both