Is it necessary to wipe the entire ear, and should new water be designated for each side if one wipes the outer and inner parts with a single finger?

Wiping the ears is among the sunnah acts of wudu, not an obligation according to the majority of scholars. Therefore, it is not required to wipe them thoroughly, and your wudu is valid even if you intentionally omit wiping them. The recommended method for wiping is to use the index finger to wipe the inner part of the ears and the thumb to wipe the outer part. However, this specific method is not obligatory, and wiping them by any method is sufficient. The majority of scholars also recommend using fresh water for wiping the ears.