there is a splice for the two power wires feeding the relay, yes. solder it for your own sake and tape it well.
the circuit should have a fuse. if you are using stock wiring, there is a fuse, if you are adding one for the 255, then put in a fuse.
the black/pink S13 wire will connect to your #2 spot in
your diagram there, if Im reading it right. This is shown in my long diagram with the relay (fsm pic) as well. see the larger version in the first page of the sticky.
also, your solid black wire with the + sign on it should not be + but ground, because if you have positive at both ends of the pump motor you won't spin the pump

that side needs to be grounded.