Hagrid's wand and wand use restrictions

[estrom2000]

No: HPFGUIDX 89051

Honey wrote:
> Parenthetically, it seems to me that since Hagrid is now "cleared of
> all charges" and apparently eligible to complete his wizard 
training,
> he could go to Olivander's and buy a new wand completely legally. 
What
> do you think?


Nellie:
I've also thought about it - it seems strange that although Hagrid's 
name was cleared, he didn't get a new wand (at least we never see him 
using one, including during the atttack at the end of OTTP), 
especially as he became a teacher at Hogwarts right away.  
Maybe there is a rule that he has to pass some exams, like OWLs, to 
be qualified to use it freely, like other adults, and since he was 
expelled in his 3rd year he has to learn a lot and, of course, he 
can't go to classes now that he's in his sixties.  I guess there is 
no actual law about who can become a professor at school, but there 
are obviously elaborate laws about wand use in the magical community.
However, it's a bit unclear whether the restriction on underrage use 
of magic is more about age (and then adult wizards who had never been 
trained anywhere could buy a wand and use it) or more about the 
completion of magical education at some accredited school.  On one 
hand we have the Weasley twins who leave school before taking NEWTs 
and apparently don't expect any wand use consequences, but on the 
other hand Hagrid was indeed not allowed to use a wand even as an 
adult because he had been expelled (and apparently Harry's wand would 
have been snapped too if he had been expelled).  Is the difference in 
the level of education, e.g. between a person who has almost 
completed the course and passed the OWLs and someone who hasn't yet?  
(NEWTs seem to be more career-oriented and different people take 
different NEWTs.)  But then we don't hear anything about students 
being allowed to use magic freely after they pass OWLs.  So what 
happens to people who, for various reasons, don't complete their 
magical education, after they reach adulthood?  Can wizards and 
witches in general use magic at their own descretion after they turn 
18 or after they graduate from Hogwarts?  And is passing NEWTs 
necessary to graduate from Hogwarts, or just for some prestigious 
jobs?  What do you think?
I also wonder, how precisely does the Ministry discern the underrage 
use of magic.  In COS they couldn't even distinguish between a house-
elf's wanderless magic and Harry's wand magic, accusing him just 
because it happened in his place of residence (like nobody could 
visit him on vacations).  How on earth do they then distinguish 
between magic done by a parent's wand and a kid's wand in a wizarding 
family?  Or even more so, if a kid took his/her parent's or elder 
sibling's wand to do some magic?  Any thoughts?

Nellie.