ORIGINAL: Popriv
Am I correct that the control horn should always be mounted with the holes lined up exactly above the hinge point?
Yes
ORIGINAL: Popriv
Connecting to the control arm on the servo, the farther away from the servo gives me more movement.
Also correct - and the opposite is true for the control horn on the elevator (Rudder, Aileron, etc) The further OUT you go, the LESS control surface movement you'll get.
ORIGINAL: Popriv
If I want the control surface to go up 3/8" and down 1/4" where to I make this adjustment?
Is this called differential? Do you have to do it with the TX or can it be done with control linkages?
Yes, it is called differential and it can be done with either the Tx (providing you have a computer radio) or with the linkages.
To do it with the Tx, check your manual because they are all different and I'm not familiar with the DX6i
To do it mechanically, Refer to the images below