[Suicide Junkie]

For the transportation minister, you need to activate the minister in the empire options-> ministers screen. You then need to give the minister control of some ships. Select the ships, and press the "face" icon to toggle minister control of the ship.

The transportation minister dosen't send the ships off immediately, but takes a turn to load and unload population.

As for research, if you've got the minister toggled on in the ministers screen, it should be fine. The ministers add their orders at the end of your turn, so you may have to wait a turn in order so see them kick in.