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I think I must have something wrong as this answer completely escapes me, please help me if you can.
36A Collection of stories to study: lawman finding killer. (8)?n?c?n?a

36 ana con da

Anaconda, killer (snake).

Ana - collection of stories
Con= study
da = DA, lawman, district attorney.

Well done gentlemen and so fast too, my thanks to cerasus and malone

You're welcome. I don't know about cerasus, but I did this crossword yesterday - so maybe not as fast as you think.

I guessed anaconda (from the letters given + killer ) then worked in reverse

Help appreciated with wordplay for these.....

45a Traveller full of ideas first to leave about now (12) - REPRESENTATIVE

20d Almost laugh uncontrollably about test for officers (9) - CORPORALS

I can see 'Oral' for test and 'Corps' for 'Officers' but just don't get 'Almost laugh'.

29d Shallow northern river - jump across it (4,4) - SKIN DEEP

It's N(orthern) DEE (River) = SKID but I'm having difficulty finding where 'Jump' and 'Skid' could be used in the others place.

40d Party skirt and cool top sported by an islander (9) - DOMINICAN

I get 'Party' = DO + 'Dress' = MINI, but why is CAN a 'Cool top' and not just a 'Top'?

29d More correctly 'Jump' and 'Skid' as synonyms.

45a RE PRESENT ATIVE
(C)REATIVE, full of ideas minus first letter, about PRESENT, now

40d DO MINI C AN
cool top = C + AN (in the clue, sported by 'an' islander)