Solution to 1D has been deliberately left unsolved and is to be answered by a non-regular/novice commenter, with proper annotation. Those who have answered earlier in the week, please give others a chance.
Open for anyone to answer, if not solved by 1 PM.
ACROSS
1 Almost relaxed about conducting children's drill (6) SCHOOL {LOOSe<=} over {CH}
4 Recurrent mistake inhibiting No.1 in Open American championship (8) ESPOUSAL {LAPSE<=} over {Open}{US}
10 Non-combatant John defending criminal vilified after disappearance of female editor (8) CIVILIAN {CAN} over {VILIfIed}
11 Following mushy, thick paella Avtaar will calm down (4,1,5,4) TAKE A CHILL PILL {THICK+PAELLA}*{I'LL}
13 Savoury can be chosen after starter for dinner (10) DELECTABLE {ELECTABLE}<=>{Di...r}
14 Ebbing river that is close to Warsaw Embankment (4) WEIR {R}{IE}{w...aW}<=
16 Show rear end of catheter removed from ass (4) MOON MOrON
18 Menacing coach upset by stragglers, finally isolated places for late-comers? (10) GRAVEYARDS {GRAVE}{DRAY<=}{s...rS}
21 Chemical from mobile charging distorted resolution (14) NITROCELLULOSE {NITRO{CELL}ULOSE*}
23 Male model exposed retrograde tendency to play favourites (8) NEPOTISM {M}{SIT}{OPEN}<=
24 Round table made flat on both sides (6) OBLATE {O}{TABLE}*
25 Confirming result briefly on phone (8) ENSURING {ENSUe}{RING}
26 Afternoon school's principal visiting faculty nowhere to be seen (6) ABSENT {A}{B{Sc...l}ENT}
DOWN
1 Deposit left in knife dropped down (4) S?L? (Addendum - SILT S(-l)I(+l)LT - See comments)
2 Spike in upwardly mobile Mongolian Bohemians (7) HOBNAIL [T<=]
3 Old coins from Britain embodying earliest signs of unusually lavish luxury (8) OPULENCE {O}{P{Un...y}{La...h}ENCE}
8 Hosts in stadium having come cycling (9) LANDLORDS {L{(-l)AND(+l)L}ORDS}
12 President Brown visited by leader in Idaho introducing a boy (11) CHAIRPERSON {CHA{Id..o}R}{PER}{SON}
13 Work out ending in Korean cinema about absolute authority (9) DOMINANCE {DO}{k...aN+CINEMA}*
19 Model again exercising. perhaps with energy, letting pressure off (7) RESHAPE {pERHAPS}*{E}
20 Siren's topless photograph linked to her missing husband (6) HOOTER {sHOOT}{hER}
22 Do without cocaine for semifinal run, say (4) HEAT cHEAT
Reference List
Children = CH, The in French = LA, John = CAN, Female = F, Editor = ED, River = R, Male = M, Afternoon = A, Old = O, Coins from Britain = PENCE, Pressure = P, Energy = E, Husband = H, Cocaine = C