No 12266, Friday 16 Mar 2018, KrisKross

Answer and anno for 22D left for a first-time commenter till 10AM.

ACROSS
1   Matchless woman performs like a top name, for the most part (8) SPINSTER {SPINS}{TERm}
5   Letters from war-torn country? (6) RWANDA  {W A and R}* My COD

9   Epitaph: "One born on 1st of April, by the riverside" (8) RIPARIAN {RIP}{ARIAN}
10 Kipling's character playing with old dress (6) KIMONO {KIM}{ON}{O}

By No machine-readable author provided. Lukacs~commonswiki assumed (based on copyright claims). - No machine-readable source provided. Own work assumed (based on copyright claims)., CC BY 2.5, Link

12 Brewed extremely light tea or coffee (5) LATTE {LighT+TEA}*
13 Vessel carrying harmful weapons (9) ARTILLERY {ART{ILL}ERY}
14 Payment, billed regularly, is inadequate (6) FEEBLE {FEE}{BiLlEd}
16 Gate pass must be won at all costs (2,2,3) DO OR DIE {DOOR}{DIE}
19 Time to return to country seat (7) OTTOMAN {T}{TO}<={OMAN}

By Mrprofdrjjjj at English Wikipedia, CC BY-SA 3.0, Link

21 In forest, unlawful to go around a tree (6) WALNUT [T<=]
23 Shower with glory, perhaps reaching this elusive target (4,5) HOLY GRAIL* {GLORY}* in {HAIL}
25 Possibly Bahrain, not an Indian state (5) BIHAR BAHRaIn*
26 Some plans were fit (6) ANSWER [T]
27 Time to give confidence to son, leaving to get a fortune (8) TREASURE {T}{REASsURE}
28 Tough and mischievous, say (6) KNOTTY (~naughty)
29 What about politician's unwarranted importance? (8) EMPHASIS {E{MP}H}{AS IS}

DOWN
1   Desperately starting to swim, hero eventually reaches bank (6) SORELY {Swim}{herO}{RELY}
2   Setter's one breaking copyright, becoming frustrated (9) IMPATIENT {I'M}{PAT{1}ENT}
3   Splurge before visiting Singapore on vacation (5) SPREE {PRE} in {Si...rE}
4   Name spoilt…had to send out (7) EMANATE {NAME*}{ATE}
6   Eddy's fur gloves, fashionable, covering both hands (9) WHIRLPOOL {W{HIP}{R)(L}OOL}
7   You need it to breathe, taking in oxygen — and it could choke you (5) NOOSE {NO{O}SE}
8   Terribly costly to go around Spain, following a group of fans (8) ACOLYTES {A}{COLYT{E}S*}
11 Ornament gathering dust (4) STUD*
15 Polite expression, yet bugs me somehow (2,2,5) BE MY GUEST*
17 Crazy after cash and sweets (9) DOUGHNUTS {DOUGH}{NUTS}

By Evan-Amos - Own work, Public Domain, Link

18 First carrier to launch a "bring-your-spouse-free" scheme? (5,3) NOAHS ARK [CD]
20 By starting to network, gets attention (4) NEAR {Ne...k}{EAR}
21 Glower at wife’s formal make-up (7) WOLFRAM {W}{FORMAL*}

By Ulfbastel - Self-photographed, CC BY-SA 3.0, Link

22 My American partners eat red vegetables (6) ?R?E?S (Addendum - GREENS {G{R}EE}{NS} - See comments)
24 Catch girl with ring (5) LASSO {LASS}{O}
25 Live long, mostly in the seashore (5) BEACH {BE}{ACHe}

GRID