Ingame splat mapping

The best way to go about something like this would be when firing, you spawn a GameObject with a Rigidbody and Collider and project it forwards. This can be a "blob" of paint. When it collides with a wall GameObject tagged with "paintable", you destroy the blob, set the paint property of the wall to the paint property that the blob had. The properties would be set in a script. Something like a WallScript and BlobScript that have variables that can either be predetermined (for the blob) or be changed (for the wall). You could have multiple blob prefabs for different colors and change those with a control.

For the painting effect, you'd probably spawn decals and changing the material of the wall. Either change material.coloror spawn in a colored "splat" decal where the blob hit the wall. That decal could be a texture that you make.

For the player moving only on certain colored floors/walls, you could set a variable in the player script for what they are currently allowed to travel on, then check the player's OnCollisionEnterand trigger a Game Over if they collide with the wrong wall.

Additionally, you could have a game manager that keeps track of the current traversable color, then disable walls' colliders that don't have that color. It would be more effective if a player falls through the map than a simple Game Over screen xD

I hope this helped, tell me if you need help with any specifics, and good luck with your game!