I am going to be controlling a large amount of neopixel buttons (maybe 100). The Arduino cannot power that many LEDs and the whole project should be powered by a single 9v wire leading to the wall. I cannot use the Arduino breadboard modules as they are rated at 700mA and each LED can use upto 60ma. However, realistically i will be using at most around 30mA per pixel for my purposes.
How can i be able to solve this so that my device which has all my components inside can be powered from one power lead? I have linked the product below where you will notice that they are individual PCB light and not connected in a strip with an power line built in.
You have to use voltage regulators to convert the voltage you have to the voltage you need. The most efficient sort of regulator is known as a buck converter. A linear regulator just burns off the excess power.
Nothing you have described so far operates at anything other than 5 V, so I cannot imagine why you would want to use some 9 V supply!
Not only that, 5 V supplies to provide this sort of power are readily available, 9 V supplies are not!
55 mA per pixel times 100 suggests 5.5 Amps, so a 5 V 6 Amp or 10 Amp supply would be appropriate. While I know computer power supplies are commonly rated to 5 or 7 Amps output and have a 1 metre or so cord to the PC, running that sort of current at 5 V over any significant distance sounds like a bad idea, better to use a supply located near your display with a mains cord to the wall outlet.
You do seem to be very new to this if you do not know how to practically connect things in parallel. Perhaps you should better describe the overall purpose of this so we can advise on the construction.