Can a ship that can donate target locks (eg Jendon) give them to a ship that cannot normally use a target lock (eg a basic TIE Fighter)?

Yes, it can.

Ok, thanks

As, for the record, can any upgrade that gives a ship the ability to acquire a TL or take a TL action. In particular, Fire Control System and Systems Officer.

If you're instructed to perform a specific action, you can do it regardless of whether it's in your action bar/cards. If you're instructed to just perform a free action without specifying what, it must be one from your action bar/upgrade/damage cards.