Venky

2. The Galilean moons of Jupiter.

— the insane nemesis of a inn-keeper's belligerent daughter = Callisto. Callisto is a fictional character in the fantasy TV series Xena: Warrior Princess. She features as a recurring villainess on that show. Xena is the daughter (warrior = belligerent) of innkeeper Cyrene.
— a parent of three posthumously-appointed judges = Europa. Europa (in Greek mythology) had three sons: Minos, Rhadamanthus, and Sarpedon, the three of whom became the three judges of the Underworld when they died.
— the alias of a forest inhabitant, exactly to your taste = Ganymede. “Exactly to your taste” = As You Like It. Rosalind disguises herself as Ganymede in the Forest of Arden, in Shakespeare’s As You Like It .
— an attention-getting shout? No, just the reverse! = Io. Oi reversed is Io.

Callisto, Europa, Ganymede and Io are the Galilean moons of Jupiter.

Venky

5. The central character is Achilles. The painting is “Achilles among the Daughters of Lycomedes” by Erasmus Quellinus II (Oil on canvas, 220 x 240 cm, Groeninge Museum, Bruges). Achilles was dressed up as a woman by his mother Thetis and hidden in Scyros among Lycomedes’ daughters.

Sergeant Dudfoot

We're in the realm of rhyming slang:

1. Cut it on a special day, north of London. = Hair - Barnet (fair)
2. You'll see one of the men from the tub, perhaps the captain. = Look - rub-a-dub-dub and all that gives us the Butcher, together with Captain Hook
3. Round the shoemaker. = Balls - Cobblers' Awls
4. Yak, one meat to eat, and one to cuddle too. = Talk - Rabbit and Pork
5. Vex, often the better part. = Wife - trouble and strife.

Granny Smith and a Spartan, and Williams and Bartlett lead us up the ligneous incline to Bedfordshire.

Sergeant Dudfoot

Lew Wallace was governor of New Mexico, wrote "Ben-Hur, a tale of the Christ", which was made into a film that starred Charlton Heston, wo was was president of the National Rifle Association between 1998 and 2001. "Ben-Hur" was the first work of fiction to be blessed by a pope. Wallace also wrote "The Boyhood of Christ".

Wallace participated in the trial of the conspirators in the Lincoln assassination.

Wallace met with Billy the Kid and offered him an amnesty in return for testifying against other outlaws - an offer that was later withdrawn.

Alan

7:  The three images are: a ferrotype of Billy the Kid, a depiction by Currier and Ives of the 1865 "Assassination Of A Man With A Beard But No Moustache", and the state flag of New Mexico, USA.

The three are linked via Lew Wallace, who (i) participated in the military commission trial of the surviving co-conspirators in the assassination of 1865, (ii) governed New Mexico 1878-81, and (iii) had dealings with, and ordered up the posse that shot dead, Billy the Kid in 1881.

Secondary links: Wallace wrote Ben-Hur: A Tale of the Christ, the first work of fiction to be blessed by a Pope, and filmed in 1959 eponymously starring Charlton Heston, who would become president of the NRA from 1998-2003.

Moreover, Billy the Kid was also known as William Bonney, so could be said to have a "Bonney face". There have been nine popes named Boniface.

The assassin shooting He Who Must Not Be Named is John Wilkes Booth. Another Booth founded the Salvation Army; its "motivation is the love of God as revealed in Jesus Christ".

The state seal of New Mexico features the Bald Eagle, as does the emblem of the NRA.

I'm sure there must be other ways of lincoln them too.

Venky

8. Brugger & Thomet AG’s B&T MP9 PDW/submachine gun, an updated/product-improved version of the Steyr TMP submachine gun (after acquiring the rights to it). The B&T MP9 PDW/submachine gun is recoil-operated and fires from the closed-bolt position. It utilizes a rotating barrel locking system. The MP9's receiver is made from a high-strength polymer that's not only impervious to rust/corrosion from saltwater, but also to damage from solvents/cleaning agents.

Todd

Brügger & Thomet MP9, with a suppressor and scope. The Brügger & Thomet MP9 is basically a Steyr TMP with a stock that folds to the right side of the weapon and has an integrated Picatinny rail. There is also a semiautomatic version called the TP9. The MP9 is developed from the Steyr TMP.

Neal

8) Brugger & Thomet TMP Tactical Machine Pistol, or the MP9
It even has its own dedicated website with a delightfully short URL: www.mp9.ch

Venky

9. Between schoolboy and scrambled eggs I find schwa; sciatica; scimitar; scion; scooter; scot-free; scoundrel and scourge.

I can also find a schooner, which is a sailing vessel, as well as a tall slim glass for beer.

Alan

10: Assuming that your four stars are an example of extreme Bowdlerization, you could be referring to the fact that Browning became an atheist at one stage, and then renounced it. More likely, though, you're thinking of his dramatic poem Pippa Passes, which contains the immortal lines:

Then, owls and bats, cowls and twats,
Monks and nuns, in a cloister's moods,
Adjourn to the oak-stump pantry!

apparently in the belief that a twat was part of a nun's head-covering. According to Wikipedia: "When the editors of the Oxford English Dictionary inquired ... where Browning had picked up the word, he directed them to a rhyme from 1660 that went thus: 'They talk't of his having a Cardinall's Hat/They'd send him as soon an Old Nun's Twat.' Browning apparently missed the vulgar joke and took 'twat' to mean part of a nun's habit, pairing it in his poem with a priest's cowl."