When I multiple out Melancolic Mercurius, do the speed buffs stack onto each other for each copy? Or does just every copy only get +2 speed?

Only the original one has the static speed pump, since multiple copies are considered to have blank text boxes. The original will be at 2 speed, but its copies will have the bonus applied to their speed.

In that case, if I play another Melancholic Mercurius after the first one, does the new original MM get +2 from the first and do the new copies get +4 speed? Or does the static ability not stack at all?

Yes, the 2nd MM will have +2 speed and each of it's multiples will have +4 speed since there are two printed copies of MM in the card pool.

Note however if you play two MMs, then all any multiples will get +4 speed and both MMs will get +2. Of course, one them will likely have resolved at the time the second MM is played, so those speed buffs will likely be irrelevent.

Stamps Ahoy.