Comparisons of both density and total population between different cities are problematic because so much depends on where boundaries that exist for somewhat arbitrary political and historical reasons are drawn. Metropolitan statistical areas sort of give you an upper bound for the latter but not the former. London is a particularly challenging case given that not many people live in the City. (Paris, and to some degree, NYC have the opposite situation where outside of the very core, density is quite a bit lower--especially with Staten Island in the case of NYC.)

Not really, because City of London is a borough of London proper and is really just the business district.

City of London is not the same as city of London.