What diagram is that? Have you posted it?
Yes, it is on the original question.
Yes, I was sidetracked on that. In my defence, the drawing is not an easy one to read, big boxes with tiny gray printed labelling. Indeed, the 5V powers the Nano directly. You called it "this" schematic so I'm not sure if it's yours, if not, did it come from another project that you can link to?
Since your stated issue is that the Nano won't work standing alone, you have two problems. You probably have to replace the Nano, and also you may destroy another one if you do.
The failure probably indicates some error in your wiring. It is nearly impossible to diagnose that kind of flaw remotely via forum. With a power distribution problem, often the technique is to disconnect all loads, monitor the voltage and/or current, and begin attaching devices one by one, until the failure exhibits itself.
For us, it's a big problem that everything is generously swathed in electrical tape. For your own sake as well, the first thing you have to do, is remove all that.
It is likely impossible to deduce the cause from the fact of a failed Nano. Instead, you have to make a comprehensive, general sweep inspection and measurement of everything.
Understandable. Here is the link to the project I was following. Github
I will remove the electrical tape and test all the devices to find out if a device is causing the issues.
I would use a breadboard like they did but DONOT connect the 3 red LEDs.
Unfortunately the breadboard won’t fit inside my project and the red LEDS are needed.
If a breadboard won't fit then there is no way you are going to cram that big mess of wires in a small space without shorting something.
You need to find a better way of doing this.
To clarify, the LENGTH of the breadboard is too long. But I have the height for the wires, and the lights extend to another section. I have tested the fit with the wires and I have room to spare for the battery pack as well.
A very crude sketch of the layout.
If I were to wire it to a PCB board, that may help with the wires issue. Would this work?
A PCB would certainly make for a neater set-up and reduce the possibility of accidental short circuits.
However, just because you found something on github doesn't mean it actually works or is correct.
Connecting 3 LEDs to one Nano pin will certainly damage the Nano, so you need to do that differently.
There may be other errors in the design as well
I would put everything together on a breadboard first to make sure it works like you think it should.
You can have, theoretically, any number of LEDs on a "pin".
The point is - If the sum of their currents is greater than approximately 25mA then results will be less than favorable.
(If you change those 220ohm resistors to 510ohms then you'll be OK.)
So if I were to switch the button LEDs of A1 and A2 (because I had removed that code) to having the two other red LEDS lit by each pin individually would I that help with the flow, if I am understanding correctly? Or would 510 ohm and keep the 3 on the same one better for the Arduino?
Yes, then as long as each pin spec is met, you only have to meet the aggregate pin current spec. But the whole point of a spec is to provide confidence within limits, if you keep one pin within spec, there is no problem.
Have you done any testing, to determine how bright your particular LED's are, at various current drive levels?
I have not done any testing on the current drive levels for the LEDS. All I know for sure about them is that I currently have the 220 ohm attached go it and that the LED has
Vf- 1.9-2.1
20 mA
λ - 620-630 nm.
So knowing that the LEDs are parallel, thats 60 mA and they have the 220 ohm (on the cathode side) on it, which is more than the 150 ohm that it should have been rated for. But its the brightness I wanted it to be.
If you have 220 ohms on each one, the pin current will be approx (5V-2.0V)/220 = 13mA. However I'm not clear whether the "brightness you wanted it to be" was with the 150, or the 220 ohm.
Also, whether what you "want it to be" is mandatory, or optional. Question was really, can you get away with less bright?
Working backwards, if the pin maximum is 20mA and you want to distribute that 3 ways you need 20/3 = 6.66mA per LED. Then the resistor per LED is (5V-3V)/0.0666 = 450 ohms.
It is the brightness wanted right now with the 220.
The brightness is the choice, so I can go a bit dimmer, but it is a clear red LED so it won’t have the casing to help it with redness. Ill try and switch it out for a 500 or 550 ohm resistor (whichever I have ) and see what the brightness does there as I do not have a 450 or enough to make 450 for 3 diodes.
Well, the 220 puts you over the maximum pin current spec. 20mA, not the widely misunderstood published figure of 40mA.
Someone suggested using additional pins. What is wrong with that?
You have a 440, if you have two 220's. 
Nothing is wrong with doing that (and I actually might just for mental sanity sake.)
And I thought it was better to go up than down on resistor values?
I thought I did go up, didn't I? If you mean the 450-440 difference, it is less than the usual 5% resistor value tolerance. The whole point was to allow you to experiment with the value and get meaningful data, with what you have on hand.
21mA is not much different than 20 in this case, it's just wise to avoid a "slippery slope" that has no end, e.g. if 21 is okay then 22 is okay then 23 is okay then 24... then 100mA is okay.
See what I mean?