2. That would have been the Lincoln Imp Railtour, Kings X to Lincoln & return! If it was empty when you saw it I would hesitate to propose it was been turned ready to run south again on the return leg. Between 13h00 and 16h45 then most passenger would be in the city somewhere.
That would have been on the Midland Railway Centre line which joins the main line at Codnor Park Jn, north of Langley Mill. 47401 was a guest loco for their 1960s weekend. Don't know which of their steam engines it was.