Re: batuu patrol
Kylo's mission that you talk about has two objectives "Disperse loiterers" and "make an arrest". There is another Mission with "Intimidate citizens" and "make an arrest". Neither involves "Go on Patrol". The only mission with "Go on patrol" I have had involved going to Black Spire and check ID of 3 Batuu citizens. If you hover over the task in the work tab you will see a description of the things you need to do to complete the objective,
I did see an example after doing an arrest that the task to escort the arrested person did not start just as you describe. The reason for the error seemed to be that another First Order Officer interfered while I was wrestling with the arrestee.
Edit:
@Truly_Rudly I finally got the mentioned objective. The trick is to go to the Spire Outpost and click on the ground. There you can go on patrol. The Order of the two objectives does not matter.