Pods cannot be ejected without a person inside them to eject it. And once an escape pod is ejected, it cannot be replaced. you Can tractor it into a docking bay, but it remains as a separate escape pod.
You go to the entrance, select "Enter escape pod", and you will get a confirmation. If you do, you will then find yourself outside the ship in an escape pod. The escape pod then works like any other fighter, minus movement if I remember correctly.
Is the Escape Pod feature actually in Position 2.0? I seem to remember people mentioning that it was missing - you should be able to access them from any of the rooms around the outside of an entity when they are activated. Doing so will spawn an Escape Pod (when its reintroduced) and put the player that used it and their party into the pod.
As for picking it up, it then counts as a fighter so yes you would need a docking bay to move it. The only way to restore escape pod counts after ejecting is to 'repair' them to recover any lost pods.
Escape Pods are restored to a ship once ejected by using the repair feature (see the relevant rules page for more information). You cannot take a completed escape pod and put it back in as it were. This is because when they are finished with, when you eject a pod it makes its way to the nearest planet and lands there then will become useless.