As for the first problem, is it possible that the mission needs a specific trait or job and the only possible options are those that they are recommending? This would prevent others from showing. Sometimes I get some odd behavior where recommendations don't show correctly and I have to click on the empty doff slot icon to the right.
For the other problems, have you checked the 3 filter options: Status, Specialization, and Quality? Status should have a check beside Reserve, Active, and On Assignment (at least, that's what mine does by default). Specialization and Quality should have no checks in order to view all options.