A few thoughts.... as a beginner myself, so I might have made a few mistakes.
LED 3 can never be lit, or is that a schematic anomaly? There is a path to bypass it regardless of transistor state so 0V will form across it. I would remove the bypass trace between D1 and the end of LED3. Also, no need for R3 as you have already current limited the circuits back at LED1/2 with 360Ohms. Note this limits the relay ON current also. The relay resistance might change the brightness of the LEDs as it will drop some voltage. Probably quite small though.
The path to "ON" has to traverse 2 transistors + 1 diode + 2 LEDs (although one of them currently won't work). So the total voltage drop could be as high as 5V, More likely 0.7*5 = 3.5V leaving 5.5V for the relay to engage with. Actually the LEDs drop much more than 0.7V, blue LED will drop nearly 3V on it's own.
Relay might need a flyback diode across the coil. The coil acts like an inductor, when energised it will hold charge, so when you suddenly remove the current from it it will might spike a large voltage backwards. D1 (and LEDs) "might" block it, depending on the coil it can be kilo volts!, but normally you put a diode reverse across the coil so the voltage just spins around in the diode until it decays. When the relay is powered current will flow through the coil. When it is off it will discharge itself backwards in a short circuit with itself.
https://electronics.stackexchange.com/questions/146499/relays-flyback-diode-is-it-necessary/146514R1 and R2, the purpose of these is to stop the large amount of current that can flow from the transistor Base to Emitter. They need to be speced to be low enough to saturate the transistor, but not much more than that. It does then beg the question, if you are limiting the current that can flow from Base to Emitter with a resistor, just so the transistor can switch the un-restricted current from the same source.... you don't need a transistor at all. Transistors are used when you want to use a lesser current source to switch a higher one. Such as from the pin of a Microcontroller which couldn't power the relay. In your case you are just using switches, which can easily supply the relay on their own.
I had a play with a schematic and the only difficulty here that can't be done with 2 switches are the LEDs for various states. However in your circuit LED5 will only light if LED4 is also lit. This can be done with switches, but I would assume you would want to have TANK_LOW, SUMP_HIGH, PUMP_ON LEDs independently.
The Arduino, being fully digital micro-controller allows you to do all this stuff in software. Although depending on the relay coil current you might need a transistor to drive it and the flyback diode. A mosfet is probably easier to deal with, a logic level mosfet will work without current limit as it doesn't pull or leak current through it's gate like a normal bipolar does through it's base.
You would then just need to connect your S1 and S2 to ground when on, floating (disconnected) when off, set the Arduino pins to internal pull up. Similar for the outputs of SW1, to ground when on. On output pins, you put current limit resistors for LEDS ( TANK LOW, SUMP HIGH, PUMP ON, RelayCoil ).
void loop() {
// Depends on whether these float switches are on (LOW) or off (HIGH) for these states.
// ! means NOT, ie, the reverse, I have assumed the switches pull LOW when on
// Set the tank and sump status LEDs regardless
digitalWrite( SUMP_HIGH_LED, !digialRead( SUMP_HIGH_SWITCH) );
digitalWrite( TANK_LOW_LED, !digialRead( TANK_LOW_SWITCH) );
// Override? Switch pump relay and it's LED on.
if( ! digitalRead( SW_OVRDE ) ) {
digitalWrite( RELAY, HIGH );
digitalWrite( PUMP_ON_LED, HIGH );
return;
}
// Normal mode, if pump AND sump are on, put pump relay on and it's LED
if( !digitalRead( SW_NORM ) {
if( ! digitalRead( SUMP_HIGH_SWITCH ) && ! digitalRead( TANK_LOW_SWITCH ) ) {
digitalWrite( RELAY, HIGH );
digitalWrite( PUMP_ON_LED, HIGH );
return;
} else { // switch them off
digitalWrite( RELAY, LOW );
digitalWrite( PUMP_ON_LED, LOW );
return;
}
}
// Remaining state is Over-ride off. No action. Although you could pulse an LED to show this state.
} // end loop
When doing a PCB one of the hardest parts is making absolutely sure your foot prints match your actual components. For example will that surface mount fuse holder fit the exact one you buy? LED 3 will never light.
EDIT: There is a bug in the code, but I'll leave that up to you to find
EDIT2: The other thing you will need is an "anti-short-cycle" to prevent ripples on the water surface and "switch bounce" from toggling the relay rapidly. Without the flyback diode this would be a good way to make a hipster aquarium switched boost converter to generate high voltage
It will also wear out the relay.