Yes, you can see on their character sheets that they have specific relation values to every person they "know", which usually progresses by being nearby. It improves extra fast for people with their favorite personality, and decreases for people with personality they hate. As a result, you would need to construct your village around the need to keep people who don't like each other's guts separate.
Villagers have sex if their relationship is 50+, they have libido, and there is a bed available. And also if there is an animation for this specific pairing.
Under some conditions, rape can also happen, but that is trickier.
You will be able to move your main base when you defeat the native boss to the north of your starting location. Main characters would have a talk and decide to stop waiting for the rescue.