Can you build a settlement in between someone else's roads?
No. If you build a new road, it must always connect to one of your own roads, settlements, or cities.
Can you build a settlement between someones roads in Catan?
Definite "yes." It is an inexpensive way to gain control of an intersection you and your opponent may be competing to build on if you have enough resources for roads but not enough for a settlement. In fact, you can even build a settlement on an opponent's road if one of your road segments intersects with it.
Can you interrupt someone's road Catan?
You are correct. You can break an opponent's road by building a settlement on an open intersection along his road!
Can you break someone's road in Catan?
Yes, settlements do break up other player's roads. If the blue player has a road that is six segments long, and the red player builds a settlement between two of the blue roads, than we say that the blue player's road is "broken". A broken road can not be counted for the Longest Road card.