Well, I'm not Miguel but I'll try to answer:
1 - They are complementary. More you can even partner them: You can run Eclipse with the Mono runtime, using IKVM. You have some efforts to make plugins to use Eclipse to develop Mono apps.
2 - Novell officialy favors Eclipse, for development, and may foster those plugin efforts. I'm not acquainted with that front.
3 - We have a nice community effort called MonoDevelop that is a Mono-based IDE, it's getting better all the time, and I'm starting to use it instead of make'ing in the console, it's just is not ready yet, and you are free to use it or Eclipse, or Kdevelop, or Anjuta, or Emacs/Vim, or just plain gedit as I'm used to.
As said you can run java apps and consume java libs in Mono, and vice-versa with IKVM, so in truth we have a great unifier in Mono, instead of a splitter...