Fire Warrior: Built around using his Pulse Rifle/Carbine and Photon Grenades as effectively as possible. Flak armour.
Pathfinder: Stealth abilities, Markerlights and Rail Rifle. Flak armour.
Earth-caste Technician: Not sure how to handle this guy. Any tips?
Air-caste Pilot: Seems a little niche for regular play.
Water-caste Diplomat: A reskinned Adept?
Kroot: Built to be sneaky and good at seeing things, plus brutal in a melee. Potentially has Unnatural stats?
The Nicassar could be our psyker with some Navigate abilities, but fluff seems to oppose that. A shame; there's art of them as squidheads, and I adore that.
Vespid need to be Strain Leaders, which kinda sucks. Probably not building them yet.
Question on Kroot Shapers; are they Psykers? Could that justify being a separate Spec?
Tarellians are my favorite xenos in all of 40k. Ideas for them?
Fire Warriors should have carapace. Fire Warrior armour is 4+ in the TT.
Pathfinders should have pulse carbines with underslung grenade launchers. A rail rifle is an absolute beast that would make the rest of the squad's weapons almost obsolete and therefore should be something to aspire to, not equipment given at char-gen.
Earth Caste are not fighters at all, and therefore I wouldn't give them any combat related Aptitudes. Maybe Agility or Srength, Intelligence, Perception, Fellowship, Tech and Knowledge. Give them some kind of toolset, a pulse pistol and a flak vest.
Should be like the IG operator. If the squad includes a Devilfish transport, a Piranna support craft or a Hammerhead grav tank he'll be useful, otherwise his usefulness is limited.
The Diplomat should be built around social interaction more than academic knowledge, so Fellowship and Social are an absolute must.
Kroot have Unnatural Strength and Perception. Exact numbers are not given in BC and OW, but I'd say (2) each.
Nicassar have no place on the ground if you follow the fluff.
Vespid, as has been pointed out, would be completely unable to communicate with the rest of the squad unless they had a Communion Helm. It would be unfluffy, but then again so is an Ogryn, Ratling or Storm Trooper in an infantry squad. However, you'd have to decide wether or not the Helm is actually a mind control device as it has been hinted at in the fluff.
Kroot shapers are not psykers. In fact, Kroot are a completely non-psychic race, though unlike the Tau they do have shadows in the Warp. A Kroot shaper would be like an Imperial Guard Colonel. Something to aspire to, not something to start as.
Funny you like Tarellians so much when there is so little info of them. I only became aware of their existance through this very thread. Info of them is scarce to say the least, so I have absolutely no idea how they could be represented.