if you carefully check Eclipse rear panel you won't see "L" or "R" next to I/Os. Just "Ch1" and "Ch2".
The unit is not exactly designed to work in full mono I/O. Infact you can choose to work in full stereo I/O or mono in/stereo out. To set mono in, go to LEVELS > I/O MODE and select Mono 1 if the connected input is Ch1 or Mono 2 if the input is Ch2.
A way to use full mono I/O is to set the unit on Mono 1 or 2 anc connect the corresponding input and output, then create presets with DUAL MONO routing and load an algorithm in the fx block feeded by the connected I/Os. Unfortunately this choice will only use a single fx block.
So your question #1 doesn't have the answer you expect. In addition to this, XLRs must be used for balanced/unbalanced line level signals (+4dB), such as post preamp, post FX loop send. Check your equipment specs for this. 1/4" connectors should only be used with unbalanced instrument level (-20/-10dB). So probably you should use your XLRs for loop send AND return. This applies to questions 3 and 4.
All outputs should be alive at the same time…but as per above, they should be properly connected to match signal type, level, impedance.
all the best