What seven segment display do I have?
For practical purposes, you will never find the datasheet for the 7 segment display you have. Especially of one that's used in a random device you are just trying to figure out. They are rarely off the shelf parts. They tend to be custom designed, or at the very list, a standard one is marked with a custom part number. The specs are under NDA. Unless you work for the company that ordered the parts, you won't find it.

That said, you can take first parts of the part number (if any is printed on the display), and look for similar ones. The pinouts are often identical or very similar. If no part number is listed, or you don't find anything, then you have to get your hands dirty. First, forget about a "standard" pinout. They don't exist.

Get a 3v coin cell battery. They have high internal resistance, so they can be used without resistors. Taking advantage of the Diode part of the LED which prevents current from flowing the wrong way, and the low voltage of a 3v coin cell, connect one side of the battery to one pin. Then connect the other side to every other pin, one by one. Have a note pad handy. You can make your own schematic that way.

The rest can be done by making a schematic of the board. Find the voltage source, find the inevitable resistors (with values if you can). Then use Ohm's law. I = V / R. By assuming 20mA and typical forward voltage drops for the color you see (~2v red, orange, ~3.2 green, blue, etc), you can figure out pretty much everything you need about it.