1. I am using keyboard to play FSX. In its settings there is an option called "Autorudder" which is enabled by default. When I disabled it then my arrow keys stop working i.e. I cannot move aircraft in any direction. What's the purpose of autorudder?

 

2. How to turn aircraft slightly to left or right without rolling?

I do highly recommend getting a joystick!  Now, I also use autorudder because my joystick has no rudder

 

function built in.  I did program 2 buttons for left and right rudder and you also have the keyboard keys

 

Numpad 0 and Enter for left and right rudder.  Using the keyboard keys will override the autorudder.

 

For a slight left turn press the Numpad 0 key once or twice and to center the rudder press Numpad 5.

 

Use Numpad Enter for a right turn.

To turn you have to roll the aircraft in combination with a movement of the rudder (called a coordinated turn). Just using the rudder will not turn it properly.

Autorudder in fsx does away with using the rudder and thus gives a coordinated turn. As the previous poster suggests you really should have a joystick it is very difficult to fly properly without one.It also needs to be a "twisty" one which you turn to simulate the rudder and also use for steering on the ground.