Does Automated Protocols do anything on these ships? One ship card only has recover and reinforce, and the other ship card has neither. Can the back half doing one of its actions grant a recover or reinforce to the front?

Yes it can. AP affects the ship, not a section.

Because it's a Free Action it doesn't have to be associated with any particular ship card or action bar.

So you could Target Lock or Coordinate as the Action from your fore section - or perform an action from an equipped upgrade card - such as RAC or WED - then trigger automated protocols to perform a Recover / Reinforce Action- then take the other action from your Aft section

Does the free Recover action enable you to spend more energy tokens to get more shields back once you have used the initial token or do you only get the one shield from the token spent? (to me it looks like the former)

The initial token is paid to get the free action. It does not grant a shield. The action then grants a shield per energy spent after the initial cost.