As I understand it, the effect of Onmi On meant that Channels are disregarded, as if they do not exist.. All data will be responded to, regardless of channel.
So yes, this means that only ONE set of parameters can be active at any one time, i.e. Controller settings, active instrument, etc, i.e. the settings that could normally be different on each channel. The data can still come in set to different channels, but the channel setting will be disregarded.
For both your specific questions, the answer will be yes.
If you play a Midi file expecting to use separate midi channels (Poly Mode) then this will result in a mess, as all notes will be played as per the latest previous settings.
All could be OK if the incoming data has been constructed/sequenced with Omni mode in mind.