Shan,
I'll try to leave room for someone else to reply to most of your message, but here
are some brief thoughts. Item 1 is interesting, but I will leave that for others to
initiate the discussion on.

Item 2:
Why are far-field triggered aftershocks larger than near-field.
Earthquakes do not cause other earthquakes to happen. Strain causes earthquakes
to happen. Once an earthquake has occurred, like the Mindanao event, most of the
local strain has been released, and another earthquake on the same rupture
plane is highly unlikely until that strain builds up again. However, strain in other
areas has not yet been released and a small amount of shaking or motion on
those far-field areas may be enough to begin the release of large amounts
of stored strain in those rocks leading to a strong earthquake. A trigger of a gun
cannot kill a tiger unless the gun has been loaded with ammunition beforehand.

Item 3:
There are cases where rain appears to trigger earthquakes or at least ground
motion. In Parkfield, CA, for instance, surface creep events commonly follow
rainstorms. This may be related to lubrication or just motion of the upper ground
following the rainstorm. Weather systems often vary the pressure on the ground
by a sudden shift from hot to cold or low to high atmospheric pressure. This has
been hypothesized as an earthquake triggering mechanism.
Another case is the strong El Nino system in the south and Central Pacific
Ocean. this causes rain and water to be sloshed up against the area of
South America, like tilting a bathtub. This increases the force on the ocean
floor over the trenches through the increased weight of the ocean water above.
This can lead to strong earthquake along the Peru-Chile area as these commonly
occur about 1.5 years after the start of strong El Nino events.
Finally, storms and rain systems can push against mountains and other
vertical structures. This may reduce the normal stress on vertical faults allowing
additional movement.
Of course, if the earthquakes are associated with volcanism, the ash and fine
particles placed in the atmosphere from erupting volcanos may act as a nucleus
for a raindrop increasing rainfall at some distance from the volcano.