Read the Novels: The Last Guardian, Tides of Darkness, and Beyond the Dark Portal. Khadgar is a primary character in all 3.
In the Last Guardian, Medivh/Sargeras doesn't "age" Khadgar completely only in looks, he was still in his late teens health wise after the incident. In the Tides of Darkness novel he tells Turalyon when asked how he would handle being in battle, that although he looks like an old man he still has the strength and stamina of a man in his early 20s. This is why Khadgar is still ticking just fine, only his appearance changed, he still has the normal health and physical abilities of someone his age.
He started doing that back at the end of Beyond the Dark Portal, in the final cinematic. My guess is that he's been fighting Medivh's curse (hence the varying apparent age), and Khadgar has finally found a way to undo it outright, so now he's defaulted back to his natural age rather than a magically-imposed one.
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I actually kinda hope that gets covered in Legion's hypothetical 5-man Karazhan update (which I sincerely hope does not replace the current raid; Blizz needs to figure out how to put in new entrances in the world map and reuse the environs in a new map). Imagine a section where there's echoes of Khadgar and Medivh's spirit (so an echo of an echo, I guess) where Medivh mentions Med'an in very rough passing, seeing as the current stance of the lore team is that Med'an left Azeroth entirely to do things and stuff of important unimportance, and gives Khadgar Atiesh, seeing as Khadgar was his apprentice and all.
Be seeing you guys on Bloodsail Buccaneers NA!