Grounding & Isolation Question

I have an Arduino that is connected to a computer via USB. Power to the Arduino is provided through the USB connection. The Arduino is controlling an LED strip light (represented with a single LED in the schematics) which requires 12V DC. I am using a p-channel MOSFET for high switching. The 12V comes from a big 12V PSU represented with a 12V and GND power in the upper left of the schematics.

My question is regarding grounding, i.e. do I need the ground connection that the red arrow on the right side points to? I believe the Arduino internally connects the GND of the USB input to the GND pins including pin 4. So pin 4 on the Arduino is driving ground for ULN2803. From reading other posts, I believe I still need to connect that ground to the ground of the PSU. Hence, that additional track from ground of the ULN2803 to the PSU. Is that correct?

Also, while this PSU is only 12V on the output side there is still a connection between something that is high current with some electronics that is low current (Arduino). Is there any concern with this? In addition, for the PSU is the ground/neutral on the AC side connected to GND on the DC side?

Yes, you must connect the grounds in unisolated circuits. The ULN2803 is darlington pair transistors, so current goes from base to emitter as well as collector to emitter. Without connecting them, there is no common reference point, or in your case, complete circuit.

What leds are you using? Do they just take a 12V input, or do they require a constant current supply?

tinman, thanks for the confirmation. These are 12V LED strips and not constant current. There are something like the one shown below, i.e. 5m LED strip with 300 LEDs. Each 2" section has 3 LEDs and one resistor. The board should allow me to control 8 such LED strip lights. For each I am going to control off, on and dimming level through an Arduino.