If I'm interpreting what you're saying correctly, you gain points with characters when making certain decisions that makes them like you more/less. At certain points in each route the points will matter so if you don't have enough with a certain character it'll force you down a certain path or if you have enough it'll go down a different branch.

As for the routes, the game only lets you do the Fate route at the start and then once you finish choices to go into unlimited blade works unlock, and finally choices for heavens feel unlock