ACROSS
1 - They are usually the first ones to greet a house guest (7,4) - WELCOME MATS [CD]
10 - Buns stuffed with clean fish fillets (8) - ROLLMOPS {ROLL{MOP}S}
12 - …and be off to find missing…. (3,4) - GET LOST {GET} {LOST}
13 - …rich variety of Bantu and… (8) - ABUNDANT*
15 - …traces of other kindred aborigines, peculiar insect species and
animals (6) - OKAPIS {O}{K}{A}{P}{I}{S}
16 - Dwelling in explicit riches, one is still sour (6) - CITRIC [T]
20 - Slogged wildly on the golf course (7) - DOGLEGS*
22 - Miss to err, man to mind and object to it? (8) - HYPONYMS [E] (Addendum - SYNONYMS [E] - See comments)
23 - Star sign containing a shrew (6) - VIRAGO {VIR{A}GO}
24 - Looks like eating soft fruit can somehow end in bellyache
(11) - APPEARANCES {A{P}{PEAR}{CAN*}{E}S}
DOWN
2 - Justify why new wife is beautiful? (7) - EXPLAIN {EX}{PLAIN}
3 - Languages test in dictation (5) - CZECH (~check) Why the plural?
4 - Ideal husband is marginally muscular and perfect (2,5) - MR RIGHT {MusculaR} {RIGHT}
5 - Gumdrop for a child! (4,5) - MILK TOOTH [CD]
6 - Lottery machine accepts million note? First-class (7) - TOMBOLA {TO{M}{B}OL}{A}
7 - Ignore redesigned brand until I say (4,1,5,3) - TURN A BLIND EYE {BRAND+UNTIL}* {EYE}(~i)
8 - An exact replica of Pieta's head in modelling picture (8,5) - SPITTING IMAGE {S{P}ITTING} {IMAGE}
14 - Original produced by artist, a revolutionary sort (9) - ARCHETYPE {AR}{CHE}{TYPE}
17 - Soldiers unit to overcome setback (7) - REGROUP {RE}{GROUP}
18 - Wrongly surmise one will treat badly (7) - MISUSER*
19 - Strong timber obtained from polished teak or elm primarily
(3,4) - OAK TREE {TEAK+OR+Elm*}