RE: as my fellow-soldiers are off duty, I'll try & help with all 7...
24a last wd is def.;1st part special kind of record (noun);2nd part "not in"
27a:hompphone for seawood + sexy support=etymology of branch of maths.
29: last 5 letters syn. for unchaste (woman-old fashioned);1st 3 prep. for prior to;abb.foot;def."before..."
16d:def. at end;word for self-interest in Latin of 3 letters;?abb for "not" outside it;+a+r.l.pest
21d:modern way of growing plants or indeed letting babies grow without much attention;cd be written 4-3 w hyphen
22d:Kasner's mathematical word for 10 to the power of 100 (think of comp. search machine);1st half = sentimentality;2nd half= cut piece of tree (I would say) reversed
25:(not sure)kind of beer; 2nd mng. "beyond the ****"=unacceptable.
Hope that helps you --- and was not too much for the setters!