Solution to 28A has been deliberately left unsolved and is to be answered only by a non-regular / novice commenter, with proper annotation. Those who have answered earlier in the week, please give others a chance.
ACROSS
1 Timeless stuff! Leader of liberals and his strange modern Indian lingo! (8) HINGLISH {tHING}{Li...s}{HIS*}
6 Dumping the starter, rush for the hot main course (5) CURRY sCURRY
10 Basic assumptions made by founders of schools, say (5,10) FIRST PRINCIPLES (~ first principals)
12 Join on promotion day (3) ADD {AD}{D}
13 Inefficiencies of one stupid teen in action (11) INEPTITUDES {I}{STUPID+TEEN}*
16 Doctor caught consuming cold drink (7) DRAUGHT {DR}{cAUGHT}
17 July's session features one of the American Civil War heroes (7) ULYSSES [T]
20 UK Bank ATM terminal upended inside resort (7) NATWEST {N{AT(m to w)W}EST}
22 Time not available? Grabs an Indian dress for Queen (7) TSARINA {T}{SARI}{NA}
24 The smart CEO created device to measure rate of progress (11) TACHOMETERS*
27 Time consuming effort to get cream (3) OIL tOIL
28 Song not yet set into notes by a composer? Something like 'i' (9,6) I?A?I?ARY ?U?B?R (Addendum - IMAGINARY NUMBER [DD] )
31 Fate of King Rama - struggles (5) KARMA {K}{RAMA*}
32 Relishes cold shack with half-chutes (8) CHUTNEYS {C}{HUT}{chimNEYS}
DOWN
2 Shining one, royal couple and a princess mostly ahead of time (9) IRRADIANT {1}{RR}{A}{DIANa}{T}
3 Tax on piece of jewellery and dress worn by strip teasers (1-6) G-STRING {GST}{RING}
4 Some ship records carrying trademark for example (3) IPR [T]
5 People from China are mostly helpful (3) HAN HANdy
6 Cheap neighbour, almost regularly in tizzy (7) CHINTZY {CHINa}{TiZzY}
7 Are you guided or controlled? (5) RULED {R}{U}{LED}
8 Approvals seen in eyes especially (5) YESES [T]
9 Switch positions intermittently (3,3,2) OFF AND ON [DD]
11 Devil starts to implement master plan (3) IMP Acrostic
14 Allow this worthy male fancy for little earthy women! (7) ENTITLE Anno pending (Addendum - {ENTITLE+WORTHY+MALE}*=LITTlE earthy womEN
15 Steward damaged iron during start of a hole (7) TRUSTEE {T{RUST}EE}
18 Spooner's person delivering goods (edible protein-rich seed) for serviceman (6,3) SAILOR BOY (~ bailer soy to sailor boy)
19 Nobody has short shopping centre forays regularly (5,3) SMALL FRY {'S}{MALL}{FoRaYs}
21 Master returned, ate bread and some steamy stuff (7) EROTICA {ACE}<= over {ROTI}
23 City of Nassau rebuilt with love (7) ASSOUAN {NASSAU+O}*
24 Opening time for Conservative figure (5) THINK (-c+t)THINK
25 Professor's cold and hot style (5) CHAIR {C}{H}{AIR}
26 No banks look at a sailor (3) TAR sTARe
29 Part of polar circle (3) ARC [T] Semi&lit
30 Unknown universal love bridges people (3) YOU {Y}{U} over {0}
Reference List
Time = T, Promotion = AD, Day = D, Cold = C, Not available = NA, King = K, Royal = R, Start of a hole = TEE, Conservative = C, Hot = H, Unknown = Y, Universal = U, Love = 0
