Monitoring of Harry's magic outside Hogwarts

[drjuliehoward]

No: HPFGUIDX 91260

We all know that the MoM monitors the use of magic by underage 
wizards outside of Hogwarts, and that Harry gets "owled at" about 
it.  One of the charges was "the use of a hover charm at 4 Privet 
Drive" in CoS.  However, Harry did not use the hover charm; Dobby 
did.  So my questions:
1) Can the MoM only detect that magic was performed but not by whom, 
thus assuming it could only be Harry?
2) Can the MoM not detect the power/presence of House Elves?  If the 
latter is the case, would that not be very useful if the House Elves 
enter the war?  Also, speaking of Dobby, he can apparate into and 
out of Hogwarts, even though as Hermione points out he is not 
supposed to do.

Julie