Does a simple casting of Detect Magic reveal the presence of magical invisibility?
Yes. And the quotation to back this up comes from the PRD glossary on invisibility where it says almost at the bottom:
Invisibility does not thwart divination spells.
If we look up Detect Magic it says plainly that it is of the divination school. Thus it can be used to detect the aura from magical invisibility.
Indirectly confirming this is the fact that the new Mythic Adventures invisibility spell specifically says:
The invisible target can't be detected with detect magic or other spells that detect magic auras. The invisibility can't be penetrated, revealed, or dispelled by spells of 2nd level or lower (such as see invisibility or glitterdust), though true seeing and dust of appearance can reveal the invisible target's presence.
It's therefore pretty clear that per the RAW, Detect Magic will indeed reveal the presence of (non-mythic) magical invisibility.
Presence, yes. But the most basic use of the spell only says that something is there, not where it is, so it wouldn't spoil the invisibility effect.
To actually get an idea of where the invisible person is, you'd have to concentrate for a couple of rounds. Two rounds is enough if the invisibility spell is the strongest in the area, but that's easy to camouflage by putting a stronger aura somewhere else. You'd have to concentrate for three rounds to be guaranteed to nail down an invisible person's location.