"Manual" isn't manual control. Manual makes them so they won't auto-run up to the enemies and attack when you input attacks or artes. Semi-Auto makes them run up to the enemy and attack, but you have full control. Auto is just that, auto. Most people play on Semi-Auto, but more advanced people, or people that really like to combo go Manual.
To set them to be your main, controllable character in battle, go to the pause menu, press right on the D-pad, then use Square to move that person to the top. They will be your controlled character in battle by default.
To link, in battle, use the D-pad. Press left to link with that person, right with the right person, down with the bottom person. You will stay linked with that person until either one of you die, or if you hit that direction again.