All pets (unless otherwise stated) are instant-cast (counts as a spell cast so cannot be cast during a combo finisher or another spell cast, but can be cast while running/mounted etc.). All faction pets will replace the Kappa/Ravager when cast and put these on a 120s cooldown, so it's either a Kappa/Ravager or a faction pet. When cast, all faction pets you know go on a 120s cd.
Listed pet damage/drain etc. is always on a testlive Straw Man or taken from the tooltip when listed as a damage range (such as Tree of Death drain), damage on mobs/players will of course differ.
Brittle Blade
Pet: Tree of Death
5m radius, affects up to two targets, drains 240-293 mana & stamina per tick and target, ticks three times over 8s
pet owner gain as much as drained, except only once per tick (so if you drain two targets you'll only gain mana/stamina from one of them)
Children of Yag-kosha
Pet: Idol of Yag
grants +20 Damage Deflection, 8s duration
Last Legion
Pet: War Machine
14s duration
hits for 537 AoE (3-4m radius) piercing damage and knockbacks targets taking the damage, 6s to load each attack so attacks twice
Scarlet Circle
Pet: Kang-Zai
30s duration
has several different attack animations, each hitting for a set amount of crushing damage
total damage output over the 30s is 1400 on average
decently sized attack cone
Scholars of Cheng-Ho
Pet: Moon Child
2s cast, pet is permanent
Changes state every 15s unless in combat or given new orders, states cycle
New Moon -> Crescent Moon -> Half Moon -> Waxing Moon -> Full Moon -> New Moon
states buff Moon Child only
New Moon -20% scale +6% damage multiplier: casts Eternal Darkness (~10m range) 3s casting time hits for 32 electrical damage
Crescent Moon -10% scale +8% damage multiplier: casts Moonbolt (~10m range) 2.1s casting time hits for 21 electrical damage
Half Moon +10% damage multiplier: casts Moonbeam (~10m range) 2.5s casting time hits for 27 electrical damage
Waxing Moon +10% scale +12% damage multiplier: melee 1.15s animation hits for 12-13 crushing damage, 3ppm on hit to do 50 electrical damage in 6m radius, AoE proc hits up to three targets
Full Moon +20% scale +14% damage multiplier: melee 1.15s animation hits for 12-13 crushing damage, casts Full Moon Buff on owner granting a 12.5s +100 Natural Health Regen buff
Shadows of Jade
Pet: The Sixth Con of Cang-Jei
grants +82 Hit Rating, +100% Fatality Chance, 15s duration
Yellow Priests of Yun
Pet: Black Lotus
7s duration, 6m radius affecting up to two targets, hits for 413 poison damage per tick, ticks three times
Pet: Golden Lotus
7s HoT healing 240-293 per tick, 3s between ticks, ticks three times
Pet: Grey Lotus
grants +320 Magic Damage, +80% Weapon Damage (melee and ranged), 20s duration
Pet: Yellow Lotus
5s duration, 5m range stun affecting two targets, 3s stun duration (giving 40s stun immunity to both mobs and players), stuns twice
Wolves of the Steppes
Pet: Demon Howler
2s cast, pet is permanent
hits for on average 10.8 crushing damage per hit, 1s attack animation