GameCube/Wii has exclusive tricks that ps2 can't do so ps2 is at a disadvantage with everything. The only advantage Ps2 has over GameCube is with Speedways which is not worth the slow loads.

Pretty sure the ps3 version is slower than GC/Wii but it may be faster than ps2 I really have no idea.. Hopefully a real answer to that question can come soon

As stated here already PS2 is really slow, It is recommended that you play on Gamecube or Wii, I belive wii is slightly faster but GameCube is perfectly acceptable!

I haven't done a run yet but I imagine Ripto Opens at a specific percentage and the gems help you reach that percentage.. that's just a guess though might want to wait for an official answer haha.