With separate wire-runs to each strip you can get-away with "reasonable" wire.
For 150 Amps, 0 gauge or 1 Gauge wire!!!! Not really practical. And at low voltages you might need heavier gauge because "every volt counts". But your runs are short so that helps to minimize the voltage drop.
Adafruit recommends a 1000uF capacitor across the power supply. That's probably not necessary with your "high power" power supply.
And they recommend a 100 Ohm resistor in series with the data line(s). I believe that's to protect the Arduino in case the WS2812 shorts-out, or maybe in-case the LED strip is not powered. Otherwise, the data-input on the LED strip is super-high impedance/resistance so the resistor isn't doing much.
It's probably not necessary. The fuse is generally there to prevent a fire or "further damage" after something else shorts-out. The power supply probably has a fuse (or something) built-in, and there is a circuit breaker for the outlet in your house/buiding.
Also, use a DMM and measure the voltage drop across the power feed wires to see what the voltage drop is.
Suggest any more than 0.3V you should consider upping the wire thickness. You can do some experimenting.
Your advice made me thinking.
I thought that will be easy to have single cable.
I saw smaller led projects and you are right, they used multiple cables.
Why this should not be a single wire?
If you're really intent on doing this with a single pair of feeds, I'd suggest running a 1/2" or larger copper bus bar up each side of the display, one side feeding the +5 side of the LEDs, the other side feeding the GND side of the LEDs.
Feed those two bus bars with 1/0 wire (or larger) from your power supply.
But, again, it's far more practical to run the LED strips with individual feeds from some form of power distribution point. That you are asking these questions tells us you've never done this sort of thing before, and haven't worked with these currents, nor the difficulties of working with the size of wire required to do it right.
Yes you are right I'm newbe to that large project and looking for help
I did testing with 5 meters strip and all is working with Arduino Mega and should work with 2500 leds.
The only thing to sort is that power connection.
Thank you for your advice.
Without knowing too much about your situation, suggest you do what myself and others have done and run something like 18AWG silicone insulated wire to strips individually.
Of course if the strip is short, its power feed might be able to be combine at another strips power leads.
Look at this chart showing 18AWG, has 150 individual strands and is 39 ohms per km 0.117 ohms per 3 meters.
Just beware! When you make connections that carry 20 amps or more, use properly sized crimp connectors and the correct tool to make the crimp. Do not use solder. A soldered terminal with high Amperes flowing through it has opportunity to get really hot and blow melted solder on equipment and people.
Thank you. That indicates the OP should use arc welder cables. They have hundreds of very fine wire strands which makes them very flexible. And they are available everywhere at quite reasonable prices. Be sure to use colored tape on the cables so the + and the - wired do not get connected to the wrong terminals!