Yeah it's an odd one alright. I don't have more then a passing knowledge of the Mechanicum, so could well have missed some nuance to the wargear/units, etc. but it seems to me there's little reason to take the Arc lance/Mag-inverter.
As you say, he's ready got the 5+ Invuln, so doesn't benefit from the Mag-inverter and who needs the Arc lance when the Arc Maul is better in melee and the Archaeotech pistol is 5 point monster. The Lance is well out classed in my opinion.
As for the Kyropatris, the field itself isn't a specific size, the effect is based off squad size. A squad of 5 benefits from the armour save reroll, while a squad of 10 benefits from both the reroll and the reduced strength of incoming shots. So the Kyropatris on the Axiarch doesn't have an effect if he's by himself, but if he joins a squad with them, then he essentially adds an extra model that needs to be removed before the bonuses are lost.
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