Each Neosegment module contains 14 RGB LEDs (WS2812B). The theoretical maximum power draw is 20mah per color per LED on full brightness according to Adafruit's Neopixel Uberguide. That amounts to 20 * 3 * 14 = 840mah per module (2 digits). In practice though, the power consumption is relatively small unless you light up all segments at once, in white, at full brightness.
For example if you are showing number "42" in blue, at 50% brightness, Neosegment would use close to 90mah in total. In most cases you should be able to safely drive 1-3 modules from the Arduino or ESP8266 power regulator without the need of additional power supply. It is recommended that you provide separate power supply if you plan to drive 4 or more modules. Neosegment is not responsible for damaged Arduinos, Raspberry Pis and other electronics. Please plan accordingly!
Honest answer: we don't know... With appropriate power supply, 20 modules connected together, capable of displaying 40 digits are not a problem! Keep in mind that it is highly recommended to have a separate power supply if you plan to connect more than 3 modules!
Each person purchasing Neosegment modules gets a special prototyping connector that looks like this:
This connector can be used to connect an Arduino / Raspberry Pi to the first Neosegment module of the chain without soldering. Just plug one end into the Neosegment module and connect the three pins to your microcontroller via jumper cables.
If you are looking at the Neosegment module face up, the top pin is +5V, middle pin is Data and bottom pin is GND (see diagram below)
Neosegment's data pin can be plugged into any GPIO pin on Arduino (you can specify the pin in software) and on pin 18 if you are using a Raspberry Pi.
Neosegment can be mounted in a variety of ways. The two 5mm long screws on the back of the Neosegment modules can be used to attach the module to a flat, thin surface. Another option is to have a press-fit enclosure that the modules would go into. Please see the reference drawing below for dimensions and distances that are important to know (all dimensions are in mm):