The most striking issue for me is how enemies can fire through every gap as if it was very clear line of sight, like small gaps in windows, past other objects disrupting vision and the only penalty is still the cover mechanic of the character being shot at where he/she is at, not anything on the path to the character.

What if objects you fire past give a penalty too, so that the more impossible shots they and you try would have additional penalties to hit, making it a bit more realistic and progressive?

Trying to get clear line of sight and positioning becoming more important that way, granted you would also have to tweak the AI more to move around more and try to get into a better position as well.

Right now they tend to just sit tight where they are and fights become rather stale.

I totally approve this idea.

For example, a penalty in damage coudl be applied for each layer of wall/window passed by the shot, for the AI and also the Player. It could help to force movement during a fight.

Definitely, that would be a great idea.

I'm no expert but I think it's more similar to XCOM system than, say, to Phoenix Point. XCOM system is based on A-to-B system with modifiers like cover and range. Basically you either have a line of sight and can shoot with an X% of chance of hitting the target or you have no line of sight and cannot shoot. In order to implement this idea I think they would need to implement a "partial line of sight", that is, adding to the A-to-B system a C, that is an additional modifier that accounts for any object along the projectile path. It doesn't sound like something you can easily patch in, especially if there is no "projectile path".

Good point - it most likely is simple just like that (like the XCOMs were - the Firaxis ones anyway). Since patch 1.0.4, I don't think it's necessary any more anyway, since if you have heavy cover between you and the enemy, then unless they're really close (or they have a sniper rifle) then you shouldn't take too much damage (possibly even none if awareness is high enough).