How to turn a fighter jet?
I think you are making things too complicated on yourself. To the best of my knowledge, fighter jet controls will in principle behave the same way as almost any other aircraft- they will in general actuate surfaces the same regardless of orientation. A left/right movement controls roll, a backwards/forwards movement controls pitch.


You would push the stick sufficiently to the right to bank until you reach the desired turn rate. You would have to maintain a little right stick to maintain the bank angle. 
As you do the above, pull back a little to ensure that the vertical speed remains zero. You also need to add a little rudder to create a coordinated turn.


See the following images taken from here and here: