If an attacking ship is at range 3 with its primary weapon and the defender gets a bonus dice, if another ship with tactical jammer is blocking line of sight this grants the defender another extra dice. If there is also an asteroid blocking the line of sight behind the ship with tactical jammer does this grant the defender a third extra defence dice?

If an attacking ship is at range 3 with its primary weapon and the defender gets a bonus dice, if another ship with tactical jammer is blocking line of sight this grants the defender another extra dice. If there is also an asteroid blocking the line of sight behind the ship with tactical jammer does this grant the defender a third extra defence dice?

Nope. You can only get the bonus die for an obstructed shot once. Range 3, through an asteroid, and through a ship with tactical jammer is still just +2 dice.

Yup. Obstruction is a binary check, not a cumulative modifier. If the target is obstructed at all, it gets a single extra die. Doesn't matter how many objects are obstructing it, it either is obstructed or it isn't, and it either gets a single extra die or it doesn't.

I thought that was changed in the new rulebook so it is cumulative?

Edit: Nope, I was wrong. I was thinking of when you fly over multiple asteroids.

An attack is either obstructed or not obstructed; the number of obstructions does not change the number of additional defense dice rolled.

Tactical Jammer is not mentioned in the FAQ at all, and only mentions that "Your ship can obstruct enemy attacks" - obstruction is clearly stated in the rules not to be cumulative; shooting through two obstacles is the same as shooting through one for the purposes of obstruction.