Is it possible to order recycler to cycle between planet and df?
So you can send and logout.

A recycling mission, you can send them to any debris field slot next to a planet. You cannot send them to an uncolonised slot's debris slot.
If there is a debris field present in the slot then the recyclers within the sent fleet will collect as much of the debri as the cargo of the recyclers can carry.

Yes, you can send the recyclers and then logout, adjust the speed on the fleet menu to make sure you are back online for when they return, to avoid having them destroyed by another player.

Once you send the recyclers they will perform one recycling mission, you will then need to send them again to perform another mission.