1 Very dry American senator in Rome once (6)
BRUTUS - BRUT US
5 Steal whiskey for large singer (8)
HAWFINCH - HALF-INCH (Cockney for 'pinch', knowaddimean?) wiv da L changed to a W. Awigh'?
9 Protestant with stringed instrument managed to capture hearts (8)
LUTHERAN - H in LUTE RAN
10 Judge’s wine imbibed by molecular biologist briefly (6)
CRITIC - IT ('It' is a rather dated way of referring to vermouth, which is a fortified white wine) in CRIC[k] - Francis of double-helix fame.
11 Arty type recalled main article, having time and energy (8)
AESTHETE - SEA reversed (main recalled) THE (article) T E
12 High wind trapping fighting men in great numbers (6)
GALORE - OR (Other Ranks) in GALE
13 Old word revealing a right rift around India! (8)
ARCHAISM - A R I in CHASM
15 Aquatic bird shot for speaker (4)
TERN - sounds like 'turn' (shot in golf or snooker, say)
17 Lamb primarily associated with priest (4)
ELIA - ELI A (first letter of associated); besides being a crossword staple, Charles Lamb (AKA Elia) is well worth reading for his gentle yet insightful reflections. His New Year's Eve is a particular favourite of mine.
19 Dealings shelved? It’s a compromise (5-3)
TRADE-OFF - a charade of TRADE (dealings) and OFF (shelved)
20 Posh headgear rejected by a North American statesman (6)
UTAHAN - A HAT reversed A N
21 Drove back the Spanish in place surrounded by grass (8)
REPELLED - EL in PL all in REED
22 Lyrical piece a Portuguese-speaking city thus presented (6)
ARIOSO - A RIO SO
23 Book couple’s got about little folk mostly male (8)
TWELVEMO - A horrible back-formation (presumably) from duodecimo: ELVE[s] (little folk mostly) M in TWO. If you're still mixing up your elves and your pixies, it's time you sat at the feet of David Brent and co.
24 Exciting item in sports programme for unfit layabouts originally (8)
EVENTFUL - EVENT (item in sports programme) F[or] U[nfit] L[ayabouts]
25 Game in farm vehicle caught by East European? (6)
ECARTE - CART in E E. It is rumoured that some people play it outside crosswords.
2 Native of Baltic State stopping debauchee’s game (8)
ROULETTE - LETT (Latvian who made his fortune producing desk diaries) in ROUE (as in eager young lads and roues and cads).
3 Islander’s cry of pleasure welcomed by famous artist (8)
TAHITIAN - AH in TITIAN
4 Desire the name of this transport across the pond? (9)
STREETCAR - this side of the pond a tram; a reference to Tennessee Williams's play
5 Fairy-tale siblings represented in Helen’s grand tale? (6,3,6)
HANSEL AND GRETEL - anagram* of HELENS GRAND TALE
6 Sack member producing dangerous weapon (7)
FIREARM - simple charade of FIRE ARM. First thing I would do if I became POTUS would be to rescind the 2nd amendment.
7 Knight of sound mind beheaded citizen (8)
NATIONAL - N (knight in chess) [r]ATIONAL
8 Eccentric had a nice ranch — in Mexico, possibly (8)
HACIENDA - HAD A NICE*
14 Turn up with baked food at church? A fine example! (9)
SHOWPIECE - SHOW PIE CE
15 Bill you reportedly delayed, set out systematically (8)
TABULATE - TAB (bill) U (you reportedly) LATE
16 Single verse cutting about deceased kinsman (8)
RELATIVE - I V in ('cutting') RE (about) LATE
17 Finally diagnose brief illness through smells? (8)
EFFLUVIA - [diagnos]E [brie]F FLU (short for INFLUENZA) VIA (through)
18 During school time it’s temporarily suspended (8)
INTERMIT - IN TERM IT
19 Poles carried in characteristic conveyance (7)
TRANSIT - N&S (poles) in TRAIT