Why does transversal magnetization decay and what is actually being measured in an MRI sequence? This may be a few questions disguised as one however this may help uncover what's the missing piece in my understanding.
$T1$ characterizes the rate at which longitudinal $M_z$ recovers and  $T2$ characterizes how fast $M_{xy}$ decays. A 90 degree RF pulse pushes all the longitudinal momentum into the transverse plane. The spins want to reach equilibrium by re-aligning themselves to the longitudinal direction, while the transverse magnetization slowly decays.
Is $M_{xy}$ decay caused by the conversion of transversal to longitudinal momentum, the spins slowly cancelling each other out because of their diverging directions, or both? From what I understood, the decay is caused by the conversion, but the signal is unreadable because of the latter and you need to send an echo signal to temporarily realign the $xy$ spins and get a reading of the total $M_{xy}$. But since it's a conversion, why aren't $T1$ and $T2$ equal, and why aren't the signals complementary?
I also do not understand what is actually being measured. Since you need to adjust the timing to change the weights of $T1$, $T2$, and $PD$, I assume both magnetizations contribute to the final signal and they cannot be separated and read independently. However this doesn't make sense for me in the weak-signal-strong-signal discussion, since a weak $z$ signal should be strong, after the echo, in the $xy$ plane and vice-versa. This means that there is some direction that is being measured, but then why not just make a second receiver so you can measure both?
Or have all sources I've read failed to mention that the operator chooses which magnetization is being read (long. vs transv.), since MRI machines cannot process both of them and still churn out a fast scan, so it's crucial to time the sequence so you get the best signal for your chosen magnetization?
 A: It is generally best to separate out different questions so that each post has one question.

Is $M_{xy}$ decay caused by the conversion of transversal to longitudinal momentum, the spins slowly cancelling each other out because of their diverging directions, or both?

Both relaxation processes happen at the same time. However, the transverse relaxation (aka spin-spin relaxation) specifically refers to the part of the overall relaxation that is caused by different spins pointing in different directions and cancelling each other.
I would not use the adjective "slowly" here since it is roughly an order of magnitude faster than the longitudinal relaxation.

But since it's a conversion, why aren't $T1$ and $T2$ equal, and why aren't the signals complementary?

$T1$ relaxation and $T2$ relaxation are different processes and they occur at different rates. From an energy conservation standpoint it is clear that $T2 \le T1$, but otherwise there is no reason to expect that they should be equal. As a rough estimate transverse relaxation is about an order of magnitude faster than longitudinal relaxation.

This means that there is some direction that is being measured, but then why not just make a second receiver so you can measure both?

We only measure transverse magnetization. Longitudinal magnetization is difficult to measure for a couple of reasons. First, it is in the same direction as the main magnetic field, but it is very small so it is hard to detect such small changes against such a large background field. Second, it does not precess so the signal from the longitudinal magnetization would be very low frequency which is more difficult to detect than radio frequencies.
So the magnetization that we detect in MRI is always entirely transverse. We detect $T1$ and $T2$ both by their effect on the transverse magnetization. So it is not a matter of making a second receiver. Instead, we need to collect our signal in different ways so that we emphasize either $T1$'s influence on the transverse magnetization or $T2$'s influence, and suppress the influence of the other on the transverse magnetization.

Or have all sources I've read failed to mention that the operator chooses which magnetization is being read (long. vs transv.), since MRI machines cannot process both of them and still churn out a fast scan, so it's crucial to time the sequence so you get the best signal for your chosen magnetization?

Again, you always read the transverse magnetization. Longitudinal relaxation ($T1$ relaxation) is not detected by reading longitudinal magnetization. Longitudinal relaxation is detected by setting up the acquisition so that the amount of transverse magnetization depends on the longitudinal relaxation rate.
