Detect Magic reveals the presence of magical auras and can provide info on the associated school of magic (I typically require an arcana check if there are several auras or other complications). However, it would not give you information about the nature of the magic or identify it as a glyph of warding. From the perspective of the user, it could just as easily be an alarm spell, or other less specific magic related to protection.
That said, there are ways to fool someone attempting to detect the glypb, such as Nystul's Magic aura which can make the glyph appear as a different type of magic or even not register the glyph as magical at all.
Detect Magic reveals the school of magic of whatever you're looking at, so no you would not confuse Alarm (a divination spell) and Glyph of Warding (a abjuration spell).
I'd ask the exact medium that spell works.
Traditionally it's sight based I tried running a halfling sorceror who used an audio or sound based version since Glyphs traditionally activate when spotted that might be me getting a little cynical
Well, if it was a spell glyph with an area spell, then just one character needed to trigger it, and everyone in the area would feel the effects, whether they could see it or not.after a DM declared everyone had to make a save against a glyph causing madness when said glyph couldn't be seen by almost half the party!