DOHC means just what it sounds like, two camshafts above the combustion chambers, advantage being you separate the load on exhaust and intake strokes off from one camshaft, meaning you split the amount of work between the two cams, and because of that you can essentially rev them higher than a traditional SOHC, just not faster. And many other things Im not getting into
Hairpin is a type of turn on a racing circuit or road course, or even a street that just has a tight full-turnaround, just like the end of a hairpin
Spooning engine is new to me, might mean spoon engine, which is a honda tuning company called Spoons racing engine
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