Hi all, have been doing some searching for the above, but not managed to find what I was after

I think I have located a pump this one arrowed here:

After a long run yesterday, when I got back I heard a light clicking coming from the engine bay, if I stuck my ear against the air filter I could hear and feel the noise coming through that. The pump shown above is attached so that would explain the noise appearing to come from the air filter! However after searching people have said that the pump for making the heating work with the engine off should be here, the one for circulating the coolant to avoid after boiling should be on the near side near the radiator, is that correct? If so I cannot find another one, anyone got any photos of where theirs is?
Also, I checked by putting the ignition on about 5mins after stopping and the coolant temp had gone way up to 100C. The fans had not come on or anything, but I could still hear the noise.
Note, I tried the heating with the engine off and it seems to work fine, no extra noises when switched on either.
So to summarise (as I am now confused what I want!):
What is the thing arrowed above for?
Where is the pump for circulating the coolant (if not arrowed above)?
Should the engine temp be allowed to get up that high after switch off?
Should the cooling fans be kicking in to cool the car?
Any way of checking the system is operating okay?
Cheers in advance, hope it makes sense and sorry for the hundreds of questions and rambling thread!
Phil
