Let me know anything I've missed. Most of this is tested.

Thanks for help in the comments:
dn, Osaka Sewers, Smaug, siscrocket21, Midnight, Dheran, Roxley, MickeyZijdey, NorthernDruid, Eraser, JerC, marc.perrin, DemocraticIcePyro

-------------------- Mechanics --------------------

Repairing:
Removes ice/fire/ACID as well as just healing you. Simple, but some people don't realise this until playing the Frozen Titans
Also removes fire/ACID from the tile you're on

Shields:
Shields work on the train to save it from attacks, but not from crashing into stuff
Shields prevent you from catching fire, being frozen, or being covered in ACID, but won't remove these effects. You'll keep taking fire damage inside the shield until you repair
You can shield the Vek although you almost never will want to

Fire:
Buildings never take fire damage, and aren't considered to be "on fire" for damage from the flamethrower weapon, even when their tile is on fire
Set pieces like the earth mover or terraformer can catch fire and will take 1dmg per turn. Renfield bombs and the train are immune to fire
Fire instantly melts frozen water tiles into regular water tiles in one hit
Fliers ending their turn over a tile on fire will catch alight

Ice:
Puts out units/tiles on fire, and turns water tiles into ice tiles
Freezing interrupts attacks, even if the unit is unfrozen again on the same turn
Frozen units can't fly, so they'll fall into chasms or water. Because ice attacks freeze water tiles, drowning a hornet requires freezing it first then dragging it into the water
Freezing the earth mover will stop it from automatically fixing chasms (usually good)
Freezing the satellites stops them from launching. Unfreezing them leaves them still with an "interrupted attack" on the current turn, but they'll try to launch on the following turn
Freezing the train stops it from moving but doesn't stop you from completing the objective (very helpful)

ACID:
Puts out tiles on fire, but won't put out units on fire
Totally nullifies the armour buff from purple psion vek
ACID-affected units which fall into water will turn the water into an ACID lake, ACID-affected units which die leave an ACID puddle behind
ACID weapons can cause ACID to tiles, e.g. over an emerging Vek
ACID projectiles pierce through shields to apply the effect, unlike ACID puddles/lakes
Vats of ACID can be pushed; when destroyed their tile becomes an ACID lake

Smoke:
Interrupts attacks for the turn, even if the unit is moved out of smoke again
Smoke prevents satellite launches (therefore failing the objective) since these are an "attack" , but won't stop the train
Puts out tiles on fire when created, as long as no burning unit is in that tile
Setting fire to a smoke tile removes the smoke

Armour:
Abe's armour doesn't stack with the natural armour of some mechs, or the purple scion buff
Armour block works on the self-damage component of weapons

Lava:
Generally the same as water, but sets units on fire
Fliers ending their turn over lava does not set them alight
Unfreezes frozen units instantly

Terrain (General):
Mountains take two hits to destroy, regardless of damage
Mountains don't take damage from fire or stormy smoke
Mountains/cities can't be hovered over, but can be flown through
The edges of the map do not cause damage from knockback

-------------------- Mission/Objective Specific --------------------

(These are mostly repeated information from elsewhere)

Shields work on the train to save it from attacks, but not from crashing into stuff
Set pieces like the earth mover or terraformer can catch fire and will take 1dmg per turn. Renfield bombs and the train are immune to fire
Freezing the earth mover will stop it from automatically fixing chasms (usually good)
Freezing the satellites stops them from launching. Unfreezing them leaves them still with an "interrupted attack" on the current turn, but they'll try to launch on the following turn
Freezing the train stops it from moving but doesn't stop you from completing the objective (very helpful)
Hornets that attack two squares at once deal damage independently to each square, which can allow them to one-shot a shielded train if it's on both tiles being attacked
Smoke prevents satellite launches (therefore failing the objective) since these are an "attack" , but won't stop the train
The tentacle squares in the final mission kill all units when they turn into lava, including mechs and fliers

-------------------- Squads/Weapons --------------------

Rusty Hunks:
Since artillery can't be fired off the map, you can't create the smoke tile behind you from certain positions using Rocket Artillery
Storm Generator damages non-Vek enemies (hostile robots), but not allies (neutral robots, buildings/objectives, pods) or terrain (ice)

Zenith Guard:
Attraction pulse can do 1dmg by pulling an adjacent enemy
The laser weapon is stopped by the first city/mountain it reaches, causing damage

Blitzkrieg:
Electric Whip, before the upgrade, doesn't chain through or damage buildings at all. Always chains to and damages stuff like earth movers or silos, avoid these missions. Solar panels, defense labs, etc, which are treated as buildings, are safe.
Boulders from the boulder mech (and any rock throwing weapons) can continue the chain from the Electric Whip, although they only have 1hp. They can also stop Vek from surfacing for a turn.

Steel Judoka:
Vice Fist doesn't work if the tile behind you is blocked

Flame Behemoths:
Flame Thrower only pushes the furthest tile when it has a range upgrade
Flame Thrower never hurts buildings (see fire section)
You can use the Teleporter on empty tiles (e.g. to move out of Scorpion webs)

Frozen Titans:
Spartan Shield does nothing to Firefly Leader, but removes the webbed effect from the Scorpion Leader
You can freeze empty tiles to freeze only yourself, although it's better to freeze a city if you can
If you're sitting in lava you can shoot the ice artillery and get unfrozen for free

Hazardous Mechs:
With Hydraulic Legs, leaping into acid applies ACID to you before the self-damage is applied, doubling it
The self-damage of Hydraulic Legs destroys time pods if you land on them
Viscera Nanobots heals you before the check for a pilot death. You also can't go into negative HP, so overkilling yourself with self-damage and/or recoil is safe, you'll still heal up to 1hp or 2hp. When you're "killed" and healed, fire/ACID effects get removed (although the tile you're on can re-apply them)

-------------------- Enemies --------------------

Shell Scions' passive (purple) is nullified by ACID (listed there, but quite important so listed twice)
Centipede spitters' projectiles hit the end tile of the map if unobstructed, allowing them to hit stuff either side of it too

Killing the Soldier Scion (green) causes all enemies to lose 1 current HP, not just max HP, which kills enemies at 1HP

Burrowers put themselves out when burrowing, meaning you have to keep setting fire to (or damaging) them every turn. They're very strong against the Flame Behemoths.

Beetles charging through a water tile will immediately stop their charge and die. The boss beetle will charge straight through water/lava, though.

The Jelly boss' attack moves it into the square it is attacking. This means when multiple jellies attack the same square, the earlier attackers will be killed

Emerging Vek can be blocked not only by other Vek/your mechs, but also by thrown boulders, and permanently blocked by a destroyed mech (destroyed mechs have infinite health)

-------------------- Pilots --------------------

Gana - if a red psion is out, deployment damage you do to other units will be healed in the initial Vek turn. It's also reduced to 0 by the purple armor scion

Isaac - if you have very high grid defense, when you're in a desperate situation that requires it you can try doing attacks that cause collateral on the building grid and hope for resists. However, the random seed for resists on a turn seems to be constant - meaning that if a building fails to resist on the first attempt it will fail to resist damage on resets as well, so don't keep retrying the same thing!