I've seen it happen two ways:
1) it creates a mini based on the minis for that continuum, but slightly different in some way. Example: In one of KittyNoodles's missions, a badfic OC organization was mis-capitalized and created a mini-monster(basically a toy car), that was a different color from the others.
2) Or, a mini based on the appearance of that OC appears. I know I read a mission with 2) sometime in the last week, but I can't find it right now. The mini-OC in that mission was a small humanoid with washed-out colors due to the OC being humanoid and the poor descriptive quality of his fic of origin, but the washed-out colors may not be universal for all smaller-OC-style mini-OCs. I'd need to find another example to make sure.

Second question: a person who creates the first mission in a continuum comes up with the mini on their own. If there are no missions in that continuum, but there is an OFU, that OFU's minis are treated as the minis for the continuum unless that OFU's minis were transformed somehow to be better or more uniform guards, which actually happens considerably more often than I thought it did when I first found out that some OFUs did that.