1, 2) The 5 V power supply (voltage regulator) on the EBB is there to provide a consistent 5V supply for the servo motor only. It is a 78M05 regulator, with 0.5 A output current capacity. The servo motor takes almost no current while idling under no load, typically about 125 mA (momentarily) while switching positions under light load, and can pull 250 mA or more, if under heavy load (for example, if the arm is blocked from turning).
If you are using this as a regular EggBot, then that leaves a maximum of about 350 mA at 5 V available for your use elsewhere. From what I’ve read, power consumption of a RPi Zero (Or really, an RPi except for the B/B+/2B) is likely to be under that number, so long as you aren’t driving any other peripherals from it that draw power. (See http://raspi.tv/2015/raspberry-pi-zero-power-measurements , for example). That suggests that this would actually work just fine. However, to truly understand the power consumption for *your* RPi, use a multimeter (or other current measuring device), to measure it under realistic conditions.
However, you mentioned the ” 700-800 mA I expect the pi to use while still driving both servos.” I do not understand (1) where the 700-800 mA figure came from (2) why the RPi would be driving servo motors (rather than letting the EBB do it) or (3) why you have two servos, rather than the one standard that goes on an EggBot.
If the total current that you will draw gets this high, you may run into a separate issue as well. The standard 9 V 1.5 A supply that we ship with the EggBot is enough to drive the EBB, its two steppers, and the servo motor. Typically, these together take less than 900 mA. However, if you are adding enough extra current draw, you might exceed the total current available from the power supply. You could compensate with a larger power supply, and/or consider using a switching power supply (instead of a regulator) to create the extra 5 V that you need.
3) As you have noticed, the current version of the EBB (v 2.3) does not actually have an alternate power jack location on the back. So far as we know, no one ever used that power jack– you are the first person that I can recall ever even asking about it — and we eventually discontinued that option.
The power (center) pin for all four servo connections is tied together. If your servo motors draw more current than is available on the 5 V rail, then you will need to provide power to the servo motors separately. A common way to do this is to use a servo extension cable, where you cut the center wire, and use that to connect the alternate 5 V power source.
4) If you have the current (2.3) version of the EBB, I would recommend soldering your wires to the pins of the power jack, where they protrude through the bottom side of the board.
“5”) The EBB does not store a full print job; it’s a line-by-line type of communication. There are some exceptions– it is possible (but not straightforward) to store a full print job in the *firmware* so that no external computer is needed. You might also consider using RoboPaint to drive the Eggbot. RoboPaint should be able to run on the RPi, has (beta) support for the EggBot, and a full API that you can use to automate the machine, at a low or high level.
