For your first question? I'm pretty sure Flaming Arrows is just a very confused spell.
Pheonix Power -> Flaming Arrows is the proper course of action for a F2 caster with 2 gems.
As to your second question?
Pretty much what Gigalith said in regards to communions.
Although be aware if a master casts a spell of a path that a slave doesn't have (Master casting a fire spell when a slave has 0 in fire for instance), said slave will get hit by fatigue HARD. (x4 penalty) This can kill slaves very rapidly if you try to do something like bootstrap Mass Thunder Strike/Skelespam if your slaves don't have the appropriate paths.
Optimal communion management involves the masters and slaves at least matching paths, although it is very much worth it to cast one or two mismatched spells, provided that these spells are CRITICAL (or at least important) to your success. (Typically army buffs or a battlefield enchant) Summon Earthpower, Relief and Personal Regen (Mass Regen is acceptable too) are also very good spells to cast even if mismatched, as those make the slaves much less likely to burn out. (Slaves benefit from any self-only spells a master casts)
BAH I TOOK TOO LONG TYPING THIS! (I'm a slow typer who obsessively goes over what I write ok?)
Thtbloves: An E2 mage CANNOT cast earthquake with Boots or similar booster, after casting Summon Earthpower they're at E3, yes, but they need 4 gems (1 to boost, 3 to actually cast) Earthquake, which is too much for them (Gem boosting DOES NOT raise your spending limit)
The fatigue issue you brought up is false, if a unit has less than 200 fatigue, any action that would kick them over 200 (Big spell, being a communion slave, massed heat auras, Stellar Cascades, etc.) will only bring them to 200. Any fatigue damage done to a unit that already has 200 fatigue will be converted into HP damage (15 to 1 rounded up ratio I think)
Of course, a unit with 200 fatigue is very much out of the fight without reinvigoration (20 turns it takes to wake up from that by default!), so try to summon earthpower first before any big spell (If it can wait a turn)
Back to Radsoc, First question Yes.
Second question usually yeah, as you can see communions can get ridiculous if you can make them very large, beware though, it's very much a eggs in one basket deal though.
Third question: Gems do not negate fatigue. Being overqualified to cast the spell reduces it (Gem Boost counts for this, so yes it does help) fatigue cost = listed cost divided by (how much the caster overqualifies + 1)
Also yes, an E2 mage with Boots can in fact Summon Earthpower -> Earthquake with 3 gems.