Did Derek finish high school and/or college in canon? Fics vary on his education, but I think he's always shown to be very knowledgeable. P.S. We love the boo way more than enough to outweigh other opinions...
Canon is very bad about being consistent involving anything concerning Derek’s history. Season five implies that he was a senior (or older) when the fire happened, but that goes along with some creepy pro-Kate retconning that happened later on, and it is very clear from earlier seasons that he wasn’t. (I generally assume he was between 15-16, and in 10th-11th grade.)
But nothing is really mentioned about what Derek and Laura did after the fire, so Derek’s education level is completely up for debate! I can personally see it going a lot of different ways, though it’s mostly dependent on Laura and what I see her priorities being.
Because Derek, post-fire? I honestly can’t see him caring one bit about finishing his education. We know what he’s like when he’s grieving – the way he shuts down, closes off, lets that guilt and grief build until it’s practically swallowing him. He chose to live in the shell of his burnt house when he came back to Beacon Hills, and then an abandoned subway station. He didn’t give himself nice things, because he didn’t think he deserved them. So I tend to believe that Laura was the thing holding Derek together in New York, making sure he took care of himself and ate right and got a job/did his school work, etcetc. If Laura pushed Derek to get his GED, he probably would have, and if she wanted him to apply to colleges I can see him doing that too, to make her happy. (And then I can see him grudgingly enjoying it, grudgingly scrolling through the course catalog, less grudgingly getting sucked in by the classes he found interesting…)
But if diploma/college wasn’t something Laura thought of as a priority, and she was more focused on Derek just being alright/getting a job/getting through each day in one piece, I don’t think he would have bothered finishing. I definitely agree that he’s knowledgable but that could have come from independent research… especially on supernatural information – can you see Derek seeking out underground bookshops and magic stores all through NYC, looking for any and all information he could find to make sure he and his sister were as protected as possible, so that what happened to their family wouldn’t happen again?
*sighs* And how much it would have killed him that in the end he just wasn’t there to protect her when she needed him…
But I’m sorry, you asked a very simple question and I fell into an enormous ramble. :P There’s no canon information on Derek’s education.