1) For signal/alien spawning, do you stop spawning signals after the signal pile runs out? Also, if your alien deck runs out but you still have signals to spawn, do you just reshuffle the aliens deck?
If you run out of signals, the next time you need to draw one, you take all the signals in the discard pile and toss them back into the cup to draw one. You never run out of signals or aliens unless stated otherwise.
2) Which dice rolls count as a 'fail'? We assumed it was the GD and the skull.
Any result which is not either a star (attack) or shield (defense). So, if you are attacking with a weapon that uses blue dice, then the shield result would also be a "fail".
3) Are the elite alien cards, like the xeno alpha that has elite moves, supposed to be randomly placed in with the others, or are the supposed to be specifically placed at certain times? Also, similarly, are the elite encounter cards supposed to be random? We didnt see any kind of distinguishing numbering system for them so assumed it was random.
I'm not sure what you're asking. The mission states what to do with each alien, whether to mix them together or hold them out for a special event. If you're talking about the elite (red) alien expansions, I'm assuming they would have rules on how to use them. I haven't received mine yet to check.
4)Our base armor has a armor shield icon. Does that mean we get one regenerating shield token, or is that just showing that it's our armor?
I think only the elite agents have regenerating armor. If the shield has a battery icon in it, it's a recharging armor shield. Non-elite agents don't have regenerating shields, at least not in the base game. The shield icon in the center of the agent card just identifies the stats of the agent's armor. The recharging shield icon will be at the bottom of the agent card.