High Power LED and relay with the same power supply
Just a few elements:


if you have 1 A going through the LED the resistor will be dissipating 6.8 W. That is a LOT of wasted power, the resistor will need to be huge and will get very hot. Resistors are not appropriate for power LEDs. You can find many easy-to-use LED drivers that would work, eg. the LDD-1000H which also supports PWM dimming and costs less than 10 EUR. That one needs a power supply at least 3V above the LED forward voltage.
Your power supply is too weak. You have 10 W for the LED plus maybe a couple watts for the servo. Add some generous safety margin and you're looking at a 15-20 W power supply if you use the LED driver. If you use the resistor (not recommended) that's 17 W for the LED+resistor so a 25-30 W power supply would be needed.
[EDIT: ok, I misread you diagram, you do have a driver for the relays. That's fine then] You must add a protection diode across each of your relays to absorb the voltage spikes that are generated when the relay operates. Also the arduino pins are not capable of driving the relays directly (too much current, that would fry the arduino), you have to add a transistor and a resistor. See here for instance.
Make sure that your voltage regulator is big enough for the relays and servo.
Make sure that the 10W LED is well mounted (with aluminium PCB and thermal paste or tape) to a big heatsink. It will burn out in seconds otherwise.


Why not two separate power supplies?