Good fun, as usual, from Slormgorm . . .
I found myself repeatedly resorting to “whimsical” as a description for the clues, with a couple of the clues being so “whimsical” that I am not sure that I could give a proper parsing for them. Perhaps we will work these out in the comments.

| ACROSS | ||
| 1 | BACK DOWN |
Support fellow over wife or chicken out? (4,4)
|
| BACK (support) + DON (fellow) around (over) W (wife) | ||
| 5 | STACKS |
Thin branches one dumped around area in piles (6)
|
| ST[I]CKS (thin branches) minus (dumped) I (one) around A (area) | ||
| 10 | COALMAN |
Fuel provider or firm with a large staff (7)
|
| CO. (firm) + A + L (large) + MAN (staff) | ||
| 11 | HEROINE |
Bit of embroidery found on horse lead (7)
|
| HEROIN (horse) + first letter of (bit of) E[MBROIDERY] | ||
| 12 | ADDICTION |
A speech broadcast in dependency (9)
|
| Homophone of (broadcast) A DICTION (a speech) | ||
| 13 | IDEAL |
Best discount offered on Apple products? (5)
|
| IDEAL or iDeal (whimsically, discount offered on Apple products, which have such names as iPhone and iMac) | ||
| 15 | AT SEA |
A meal in which there’s salt on the main? (2,3)
|
| I think this parses as: semi-&lit and A TEA (a meal) around (in which there’s) first letter of (on the main) S[ALT], where “on the main” is also the definition | ||
| 16 | ACHILLES |
Relax in NHS unit with small, weak-heeled bloke (8)
|
| CHILL (relax) inside (in) A&E (NHS unit) + S (small) | ||
| 19 | EINSTEIN |
One German mug or a Genius from Germany (8)
|
| EIN (one [in] German) + STEIN (mug), with a capitalization misdirection | ||
| 20 | BITER |
You might say Dracula’s resentful half the time (5)
|
| BIT[T]ER (resentful) minus one T (half the time) | ||
| 21 | CHESS |
Revolutionary shows (not How or The Mating Game) (5)
|
| CHE [Guevara] (revolutionary) + S[HOW]S minus (not) HOW | ||
| 23 | DAMNATION |
Madonna goes mad about SEX retrospective denunciation (9)
|
| Anagram of (goes mad) MADONNA around (about) IT (sex) reversed (retrospective) | ||
| 25 | AFFRONT |
A show heard on the radio in Diss (7)
|
| Homophone of (heard on the radio) A FRONT (a show), with a capitalization misdirection | ||
| 27 | VIOLIST |
Foremost of strikers tackled by new Tivoli player (7)
|
| First letter of (foremost of) S[TRIKERS] inside (tackled by) anagram of (new) TIVOLI | ||
| 28 | SPRITE |
Place to eat pricey rice starters or a brownie? (6)
|
| SITE (place) around (to eat) {first letters of (starters [of]) P[RICEY] R[ICE]} | ||
| 29 | PRISONER |
Crooked person: one inside tower ultimately? (8)
|
| &lit and {I (one) inside anagram of (crooked) PERSON} + last letter of (ultimately) [TOWE]R | ||
| DOWN | ||
| 1 | BACCARAT |
Grad joins cricket club with a singer to get a game (8)
|
| BA (grad) + CC (cricket club) + A RAT (a singer) | ||
| 2 | CLANDESTINE |
Secret tune in Let’s Dance (11)
|
| Anagram of (tune) IN LET’S DANCE | ||
| 3 | DEMOCRATS |
Party animals protest jazz fan stopping bit of revelry (9)
|
| I cannot quite work this one out. I can get this far: DEMO (protest) + CAT (jazz fan) around (stopping) first letter of (bit of) R[EVELRY], but I cannot see where the “S” comes from. “Jazz fans” would work. I am taking “animals” here as a whimsical reference to something like “political party members.” Just “party” would also work as a definition for DEMOCRATS, but then I cannot see any function for “animals.” | ||
| 4 | WONGI |
Leaders of West offer nothing good in informal chat in Australia (5)
|
| First letters of (leaders of) W[EST] O[FFER] N[OTHING] G[OOD] I[N] | ||
| 6 | TORSI |
One’s rubbish will be brought up in trunks (5)
|
| {I’S (one’s) + ROT (rubbish)} all inverted (will be brought up) | ||
| 7 | CHI |
Greek character rebuked after duke’s disappearance (3)
|
| CHI[D] (rebuked) minus (after . . . disappearance [of]) D (duke) | ||
| 8 | SPELL |
Period of pressure in market… (5)
|
| P (pressure) inside (in) SELL (market). I cannot see that the “. . .” between 8D and 9D signifies anything with the wordplay in the clues. | ||
| 9 | CHIN-CHIN |
…hits your health! (4-4)
|
| Double definition, the first being CHIN (hit) twice, and the second being a toast | ||
| 14 | ELECTRICIAN |
Tradesman whose shoddy work might shock you? (11)
|
| Cryptic definition | ||
| 16 | ANECDOTE |
Oscar won by new version of a decent yarn (8)
|
| O (Oscar) inside (won by) anagram of (new version of) {A DECENT} | ||
| 17 | LABRADORS |
Bounders in coats and bra or lad’s pants (9)
|
| Anagram of (pants) BRA OR LAD’S, presumably referring to a retriever | ||
| 18 | URINATOR |
Run riot messing around with a goer (8)
|
| Anagram of (messing around) {RUN RIOT + A} | ||
| 21 | CHAPS |
Dudes that cowboys might have on? (5)
|
| Double definition | ||
| 22 | SPORT |
Venue in which you’ll see runs in cricket? (5)
|
| SPOT (venue) around (in which you’ll see) R (runs) | ||
| 24 | MOVER |
Flash vicar knocked up? I’m likely to propose! (5)
|
| MO (flash) + REV. (vicar) inverted (knocked up), presumably in the sense of e.g., legislation | ||
| 26 | FAR |
A good way of finally getting to Arkansas (3)
|
| Last letter of (finally) [O]F + AR (Arkansas) | ||
Pop in for a cuppa and a bit of a wongi. It’s so long since hearing this in the wild that I have no actual memory, but it’s Aussie slang alright. Fun puzzle, ta both.
… @1 cont, … origin in regional WA, deriving from an indigenous word meaning speak [from Google AI]