Non inertial
It isn't clear what you mean by "its" inertial particle. There is no inertial particle associated with the photon.
An inertial frame of reference = constant vel. non inertial frame of reference = acceleration
If the object is falling down, it is accelerating. "Inertial frames of reference" do not include acceleration, so the falling object can't be considered an inertial frame of reference, according to the Special Theory of Relativity. However, the General Theory or Relativity explores additional complications due to gravity. In any case, if you wish, you can use the object accelerating downward as a reference frame (just don't call it "inertial"); in this case, obviously the room is accelerating upward, compared to the falling object. It all depends what object you choose as your reference frame.
Inertial confinement fusion
newtons laws are always valid in non inertial frames
Only in inertial reference frames.
Yes, as long as the light is passing through vacuum.
No, if both persons are in inertial frames of reference the situation is completely symmetric so the 'paradox' does not occur. Also note that it is not really a paradox because general relativity has a conclusive answer to what happens to the twins. It is; however, not possible to set up a twin paradox-like situation with neither twin never leaving an inertial frame. This is because if they want to move apart, and come back again, they need to accelerate somehow, and the act of acceleration causes you to leave an inertial frame.
It says that the speed of light in a vacuum measured in any inertial frame of reference is equivalent to the speed of light in a vacuum measured in any other inertial frame of reference.
It's unfortunate that this system does not allow mathematical notation, so these have to be at least partly spelled out. Some definitions: t0 refers to time interval as measured in an inertial frame t refers to the relative non-inertial time measurement m0 and m for mass, and L0 and L for length (along the direction of travel) follow the same pattern t = t0/the square root of [1-(v/c)2] m = m0/the square root of [1-(v/c)2] L = L0{the square root of [1-(v/c)2]} The lorentz transformations, by definition, compare the relationship between non-inertial frames and their designated inertial reference frames.
Non inertial
It isn't clear what you mean by "its" inertial particle. There is no inertial particle associated with the photon.
Answer this question… inertial confinement fusion
In physics, frames of reference are points of view from which observations are made. Some types include inertial frames, where Newton's laws hold and there is no acceleration, non-inertial frames, which are accelerating or rotating, and observational frames, which are defined by an observer's position and motion.
An inertial frame of reference = constant vel. non inertial frame of reference = acceleration
If the object is falling down, it is accelerating. "Inertial frames of reference" do not include acceleration, so the falling object can't be considered an inertial frame of reference, according to the Special Theory of Relativity. However, the General Theory or Relativity explores additional complications due to gravity. In any case, if you wish, you can use the object accelerating downward as a reference frame (just don't call it "inertial"); in this case, obviously the room is accelerating upward, compared to the falling object. It all depends what object you choose as your reference frame.