|Comes From||Spirit Island (Base Game)|
|Affected By||Badlands , Disease , Isolate, Strife|
TOWNS: 2 Health
You're counting pieces. "Invader" in the Glossary is defined as "A City, Town, or Explorer", so a land with three Towns and a City has four Invaders in it. (A few effects instead key off of "N Health worth of Invaders", and in those cases Towns and Cities generally count for 2 and 3, respectively.)
Similarly if checking if Dahan "outnumber" Invaders, you are counting physical pieces.
Always, regardless of how it's destroyed: directly via a Power that says to destroy one, from damage done by a Power, from damage done by Dahan counterattacking, due to a Spirit's special rules, from a Fear or Event card, etc. [p. 18]
Fear from destruction is independent of any explicit Fear the Power does - e.g., Lightning's Shatter Homesteads reads "1 Fear. Destroy 1 Town." It will usually generate 2 Fear: 1 explicitly, and 1 for destroying a Town.
Note that when you remove or replace a Town or City, it does NOT cause any automatic Fear. Removing Invaders happens most frequently via Fear Cards, and usually represents the Invaders fleeing, which doesn't make them any more afraid. Replacing an Invader represents some sort of transformation or change; if it's a scary change, the effect will explicitly specify how much Fear to do.
It means "pieces of either or both types" - you are Pushing up to 3 pieces; those pieces may be Explorers and/or Towns. Similarly, "1 Damage to each [Town]/[City]" means "1 Damage to each piece that is either a Town or a City". (Or, in theory, both - though this would require some bizarre new piece considered both a Town and a City in order to be a relevant case.)
This is described in the reference on the back cover of the rulebook. (Formally, the slash is a union operator.)