In the first movie, Connor does in fact defeat the Kurgan with heart, soul and steel, as Ramirez says: He's saved by his lover Brenda (heart), demonstrates courage, skill and care for others (soul), and bests the Kurgan in a swordfight (steel).
The only scar sported by an Immortal is the one on the Kurgan's neck, after his head his nearly severed by Ramirez. Since beheading is the only way to kill an immortal, it makes sense that their necks don't heal as completely as the rest of their body.
The Kurgan's loutish behavior in the church in the film. While his savage and thuggish personality is an obvious reason for this, there is another reason Unlike Connor, who was born into a Roman Catholic society in the early 16th century, the Kurgan was born more than a thousand years before the coming of Christianity. As such, he would consider Christianity as just another glorified cult created by mortals fearful of death. Nonetheless, though he doesn't take Christianity seriously as such, even he still recognizes churches as holy ground and won't fight in them.
In the first episode, Connor tells Duncan someone should keep an eye on Richie after Richie witnesses a duel. Duncan agrees and it's how he ends up taking him in. When watching the show the first time it comes of they need to keep an eye on him because he knows about immortals. But the meaning changes after Richie becomes immortal. Duncan and Connor both knew Richie was pre-immortal and that's Duncan took Rich in so he could teach him if his immortality was awakened.
Duncan is just four hundred years old, and yet he is consistently able to defeat immortals that are ten times older than him. Then we see in a flashback about how Duncan got his first Quickening, an older immortal sacrificed himself to give his power to Duncan. We don't how old and powerful that Immortal was. For all we know he could have been as almost as old as Methos.
The idea of a newborn baby that is pre-immortal being violently killed via some method other than decapitation. They regenerate but never age. Maybe they eventually grow mentally? But they're physically an infant. Forever.
This is discussed in a story in the book An Evening At Joes where Methos and company come across a baby who became Immortal after they raided a village. One of them does kill the baby.
Remember Tessa from season 2, who Duncan proposed to immediately after remembering a gypsy telling him that he would love many women, but never marry? In an attempt to Screw Destiny, Duncan may have actually cosmically caused her death.