Q:

Delayed choice quantum eraser for communication

I know entanglement communication is kind of the "perpetum mobile of quantum mechanics" but I still can't give it up. 
Here's a setup:
Make 10000 entangled photon pairs at T0 and let them loop in isolation. The signal photons stay on Earth with Kimbal. Elon takes the idler photons to Mars.
On Mars, instead of using 50/50 beam splitters at BSb and Bsa, Elon chooses to to use 100% mirrors to reflect either into D4 and D3 (producing a clump pattern => sending a 0) or not use mirrors and let them pass on to D2 or D1 (producing an interference pattern => sending a 1). At T1, Elon lets all the 10000 photons either to (D4 and D3), or to (D2 or D1). 
On Earth, at T1, Kimbal lets his 10000 photons hit a screen. If he gets a clump pattern, then Elon will have sent a 0, if he gets and interference pattern, then Elon will have sent a 1.
Questions:

When Elon chooses to use 100% mirrors instead of 50/50 beam splitter at BsA and BsB, does making this choice already cause collapse?
Why won't this work, theoretically?
Elon's local time is in the past compared to Kimbal's because he was travelling at a faster speed for some time, so at T1 he will be sending messages from a different timeframe relative to Kimbal's. I don't see why this is a problem, considering how the delayed choice quantum eraser experiment throws time out of the window anyway.
As far as I understand, it doesn't actually matter WHEN Elon or Kimbal make their measurements, the photons will still know whether or not to make a club or interference pattern. So Elon could have made his measurement at T1+1000 years, but Kimbal would still get the corresponding pattern at T1.

A:

The error is that Kimbal will never see an interference pattern, regardless of what happens with the idler photons that Elon has. The BBO splitter in the front of the slits changes the results that you would obtain in the absence of it (with non entangled photons you will see an interference pattern).The splitter changes the phases of the photons and the interference pattern for each photon is shifted depending on the path it went, see $R_{01}$ and $R_{02}$ below. Thus no interference pattern is observed at Earth even if the which-path information is non-existent. You can only recover the interference pattern only a posteriori, after Elon has sent to earth a signal telling which detector each photon hit, and plotting those photons on different graphs.

