Using 2nd edition rules:
1. That is correct.
2. In your example, the model shooting at an engaged tile would suffer a minimum -10 penalty to RS, because the target is engaged. If there are any other ENGAGED tiles OCCUPIED BY AT LEAST 1 MODEL in the way, the shooter would suffer an additional -2 for each ENGAGED tile that has at least 1 enemy model on it.
3. Wow, good catch. The Ping! ability specifically says it provides line of sight, but flamethrower says it can be used without line of sight if Ping! is active and within its legal range.
In my mind, It all comes down to, "Are you drawing LoS for the flamethrower when using Ping! to allow the Marine to, for example, shoot around a corner?" Pretty sure the answer to that is no. You're not actually drawing LoS; Ping! simply says you have it when using Flamethrower or Grenade.
If you using Ping! To "see" through an air duct, again...not actually drawing LoS. Ping! simply says you have it. So based on that reasoning I personally think it would work.
I have some problems with understanding rules of ranged combat.
1. If a marine makes ranged attack against a predator, who is engaged in close combat with an alien, this marine has -10 modifier to his RS test. But if a marine is engaged in close combat and makes ranged attack against an enemy in another tile, this marine has only -2 modifier to his RS test, is it right?
2. May a model make ranged attack from a tile adjacent to a fully occupied and engaged tile if the target is on this fully occupied and engaged tile? What modifiers should be used if a player wants this model to make a ranged attack targeting any other tile?
3. May a marine with a flamethrower make such maneuver: the model starts its turn on a tile adjacent to air vent tile, and there is a model with a motion tracker on the same tile. This sly marine with a flamethrower makes a move action into the air vent tile, then makes a ranged attack targeting a tile adjacent to the air vent from the other side, and then, finishes his activation and returnes back to the tile he started his turn.
Maybe these are stupid questions, but I'm not good in English, so it's very hard for me to understand some parts of rules, and I'll be very grateful for help and answers!