Mage Scribe Chakal here. Let's look in the Royal Archives for your answers.
Over the course of Calormene history there have been a number of internal power struggles. Approximately one in three royal successions were contested in some form or another leading to violence. There were five full blown civil wars such as the War of Kadesh, the two Jarisite Conflicts, the War of the False Artiban, and the strangely named Apple Blossom Crisis.
In addition you are too used to staring at the map of Terra (the World) and thinking of the whole as Narnia. In fact Narnia made up less than 1/5 of the inhabitable parts. It's the bits you don't see to the North, West and South on the map that throw you. In addition to what you see in the Chronicles, there is a City State of Terebinth, a northern wasteland of Thule, a western mountain kingdom of Jardonia and the various small provinces of Lagri, Dobril, Omri, Deligath and Transestivaal.
It has been our interest to secure the independence of these small realms, some of whom border on the edge of the world. We do not militarily intervene but we do send them materials they need to defend themselves, and the trade routes are kept open by the Knights of the Soverign Order of Saint Chesired, nominally independent and made up of all the member nations, but many of which were battle hardened Narnian warriors.
The war against the White Witch was literally one population against another. Everyone that could bear a weapon came running. She herself called up the people of the toadstools and the hags and whatnot. The fact that the war was fought using a lot of amateurs explains, for instance, why neither side used the classic "pincers" manoever...outflank, surround, close in. The commanders used the raw courage of their relatively green armies and two walls of folks basically collided and hacked away at each other. The White Witch actually had the advantage. Her army camped along the ridge and therefore was on higher ground. Charging downhill gives an advantage in traditional warfare. The other side, having to run uphill, is not going to have it as easy. That's what almost cost William the Conqueror the Battle of Hastings in 1066. But like ol' Billy the Conqueror, the brave Narnians kept plugging away and eventually won. With, of course, some help from Aslan and the additional army he brought that could attack the Queen's ranks from the BACK. Oh, and these folks got to run DOWNHILL making their rush doubly devastating.
Yes, there were lots of clean-up campaigns aimed at rooting out the baddies. While there was no organized resistance after Jadis died, there were some malevolent creatures that wanted to get back their former legal standing and rights under Jadis. They were not about to be honored as citizens of the realm they tried to overthrow through treachery and blood. Hags, ogres, and the Peoples of the Toadstools never became citizens again...EVER. As such they were not entitled to legal protection though there was never an organized campaign of genocide against them. The wolves got back the right to be citizens after 10 years IF they swore an oath of allegience to the crown. Many did. The few that refused did not cause much trouble though some lived as outlaws and committed petty thefts.
Hope that helps.