What happens when an Allie would take strain in a mission? Do they just take damage? Also, if an ability forces rebel figures to take an insight test or take damage, do they automatically damage allies? I found nothing referring to this in the rules reference guide.

Allies take damage instead of strain. The rules say that regular allies fail automatically while elite allies receive 1 success automatically. This is under Attribute Tests on page 7 of the RRG.

What about on the flip side of this. Say for example an allied figure involuntarily has strain removed from say Adrenal Stim. What reason would an allied figure recover strain? It seems to me that if an allied figure can lose health due to involuntarily taking strain, then the adverse of this should be true as well.

Only heroes can recover health by recovering strain. See Recover and Strain from RRG.

Also note that if an ability says to remove strain, it does not let the hero recover damage for each strain not recovered. You need to have the recover keyword for that.

(In skirmish figures can avoid taking strain by discarding command cards from the top of their deck.)

Allies don't have an endurance value. They can choose to suffer strain converted to damage or take an evade for Prey Upon Doubt.

Oh my, what a list of random but useful things above...