Does wearing an earpiece under the khimar after performing wudu and before renewing it constitute a removal that prevents wiping over it later? And what is the correct method of performing wudu and wiping over the khimar?

Hanbali scholars permit wiping over the khimar (head covering) by wiping most of it, if it is wrapped under the throat and is difficult to remove, and it is not obligatory to wipe anything of the head along with it. Inserting an earphone is not considered removing the khimar and does not invalidate wiping over it. Wiping part of the head and then completing the wiping on the khimar is something that is permitted by scholars other than the Hanbalis. Wiping part of the head is sufficient according to the Shafi'is, and likewise the Hanafis if the portion wiped is a quarter of the head. A narration among the Hanbalis also considers it permissible to limit oneself to wiping part of the head as well. What you are doing is sufficient according to many scholars because you are wiping part of your head, and even if you were to suffice with wiping over most of the khimar, it would be sufficient for you if it is in the manner that permits wiping over it.