A homemade campaign can be very different from group to group. There's no telling what the level of optimization or houserules your DM is using.
Both of your character ideas sound fun and cool, but there's no real way to tell if they're strong enough.
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Should be fine, a lot of the creatures can fight normally on the summon monster list, some have shadow specific abilities but not that many of them.
I mean a young umbral dragon can fight most things without difficulties.
Of course no idea, what the shadow lords are supposed to be, could just be people using shadow creatures, people from the plane of shadow etc...
Centaurs are a poor option. Their size is a disadvantage for everything but combat maneuvers, which aren't a warpriests' forte. You have to pay a feat tax to use a lance as if you were mounted and can't otherwise make use of mounted feats. Don't do it is my advice.
A shadow caller summoner might well do well; not enough info to say for sure. Note that if you summon creatures with the shadow template their SR will occasionally be a pain when buffing them.
Will a LG minotaur war priest be better?
If you're using the monsters as characters rules with the standard minotaur, then yes, though it will be carried by the 6 monstrous humanoid HD converting to 4 'levels' rather than by the warpriest.
If you're using this 3rd party version then maybe; your offensive ability will be fine but your defense and non-combat ability will suck.
If you're using some homebrew race then I can't comment without seeing it.
The fetchling shadow caller is probably fine, just concentrate on debuffs if you favor the summon monster SLA or on buffs if you favor the eidolon and it should work.