What you've been sent is the radiator for the diesel variant - as opposed to what appears to be the 1.25l Zetec petrol engine in your first diagram.
You're correct in that the "main" radiator connections are the same between the two (Despite the confusing placement of the lower hose on the second diagram it is the same hose and hooks up in the same place ...
Probably not, most likely it will find some cavity and remain there for the life of the vehicle. However it is full of fuel, if it were get close to a heat source the results could be bad.
Often handbrake covers are removable, it depends on the car how much work it would be. You could try and use a magnetic pick-up tool to retrieve it as well.