Well done for all the imagination and work that went into this! I have got a few comments, but these are just my opinions, and I may well have the wrong end of the stick in cases.
Ares - Divine Powers
Pestilence: Nice concept, however I'm uncertain about the cost for only a 20% increase. Both rare and epic versions of the Reduced Recruitment Times token would more than cancel out the negative effect (assuming both use the base recruitment time), and are easily available from quests. It also requires you to know where the target player is rebuilding troops, thus making it harder to use effectively. Would this spell impact ongoing recruitment orders, or only recruitment orders added during the duration of the spell? The answer to that changes the value significantly, in my opinion.
Warriors' Courage: I'm always cautious about the ability to increase the amount of BP gained in a battle, due to the continued possibility of farming BP from friends as opposed to fighting actual enemies. I'm assuming that this is a spell cast on an outgoing attack, as opposed to on a city to benefit from a defensive battle? I think 475 favour for a 7.5% increase minimises the abuse potential effectively.
Centurion: Nice spell, however I think the favour cost would need to be increased a little (or the number of hoplites decreased a little). Divine Sign costs 12.5 favour/population, while Patroness costs 12 favour/population. Given the similarities with Divine Sign (certainty of units given, versatile unit type), I'd say that the favour/population ratio should be about the same. (Currently Centurion has a ratio of 10 favour/population.) Patroness should arguably be the lowest favour/population ratio due to the uncertainty in results and the mixed nature of the troops given, so a favour cost of 125-130 sounds more reasonable for Centurion.
Man at arms: Another nice concept. The favour cost seems fine to me, but as I'm not knowledgeable about coding, I'm not sure how applying the spell multiple times would work. (Currently it is impossible to duplicate duration spells on cities.)
Hermes - Divine Powers
Sparta's Cavalry: I like the idea of more spells to boost specific units, but I worry that this is perhaps a little wide-reaching. It's the same level of combat boost as Artemis' Aim of the Huntress, however it is applicable to a much greater number of unit types: AotH works only on slingers, catapults and archers(!), not on mythical units with a ranged attack. I haven't analysed your new myth unit statistics, so I can't judge how much of a power difference there is, but I'd be tempted to say that the cost should be a little higher if including all those mythical units, or a little lower if just for horsemen and chariots.
Motivation: Another nice concept, but I think the cost is a little too steep for a 10% boost, given the prevalence of 25% and 50% construction boosts from quests.
Winged Sandals: No suggestions here. High cost and lower percentage than Atalanta means it doesn't risk being overpowered in my opinion.
Hippeis: As with Ares' Centurion spell, the favour/population ratio is lower than the existing troop spells (Hippeis currently costs 11.1 favour/population.) However the inability to use this spell defensively could justify this lower cost, given that emergency defence is one of the main uses of Patroness and Divine Sign.
I haven't gone over the statistics properly for each of the units yet, so I'll be looking more at the special bonuses than other values.
Erinyes: Slight optimisation of it's purpose, the fact it's restricted to land means that doesn't seem unreasonable. I would however comment that Erinyes fit significantly better with Hades from a mythology perspective.
Satyr: Interesting special mechanic - better than slingers when the wall is high, but with a favour cost to balance it out. I could see this being popular on revolt worlds (particularly fast worlds where favour production is high enough to build reasonable numbers of mythical units), but I'm not sure it would get much use on conquest worlds. (Not that a difference in mythical unit prevalence is necessarily a bad thing, given that flying mythical units are significantly more valuable on conquest worlds.) Traditionally associated with Dionysus, but nothing against using them for Hermes given that Dionysus isn't present.
Centaur: Rather serious role reversal for this unit, which I imagine would cause a significant change for revolt players (where mythical defence is easier to use). Is there a maximum percentage for the bonus? (2000 population of centaurs would gain a 50% attack bonus if there isn't a cap, and this could then be further buffed with Sparta's Cavalry for a 65% bonus before heroes are factored in.) The wisdom associated with centaurs would generally lead to them fitting better with Athena from a mythology perspective.
Leviathan: Combination of transport and combat roles definitely makes this an interesting unit. Would the transport capacity be impacted by the Bunks research? (Players would also have to consider that land units being transported by a Leviathan would then be vulnerable to drowning as a result of Sea Storm, but having to make decisions like that isn't a bad thing in a strategy game.)
Minotaur: Nice to see a reason to use an often-sidelined mythical unit like the minotaur. Would this boost be capped at a specific value?
Cyclops: Wall damage is certainly a fitting bonus for cyclopes (as much for the link to Poseidon as god of earthquakes, as for their own size and strength). Out of curiosity, would they benefit from the Stone Hail research?
Medusa: The anti-myth bonus is nice, but the serious reductions in attack and blunt/ranged defence and increase in sharp defence seems to turn it primarily into a Manticore counter (i.e. what the centaur currently is in-game).
Nemean Lion: The boost is a little confusing: does it boost attack or defence? (Defence would make more sense with the mythology, in my opinion.)
Hades' Shade: These would likely usurp Harpies as the standard harbour check unit (slightly slower, but much cheaper in terms of both resources and favour). The only thing I'm a little concerned about is favour-farming: they can loot more favour than they cost to build, and I'm not sure if that leads to any possibilities of abuse. (Fortunately they aren't quite so extreme as to actually be profitable to build and then kill with Heracles, as that was my first though in terms of possible abuse.)
Calydonian Boar: The idea of a combat transport is again interesting. I'd be curious as to how it would interact with Zeus' Rage (do all units being carried get killed if the boar is killed?). The combat value changes seem to turn it into more of a generalist unit as opposed to a powerful defender. While that might be helpful for CS waves on conquest worlds, it would also seriously decrease their viability on revolt worlds, I believe.
Once again, these are just my personal opinions, so feel free to take them or leave them as you see fit. Everyone has a different vision of what they think is good.