What is the ruling on starting wudu while resisting the urge to pass wind, given the frequent release of gas, and is it obligatory to wet the entire hands when taking water to wipe the head and ears?

There is no harm in performing ablution (Wudu') while suppressing gas, as long as nothing is discharged. Similarly, the prayer is valid according to the majority of scholars. However, it is preferable to relieve oneself first.

For wiping the head (masah al-ra's), it is only obligatory to moisten the palm of the hand. It is not required to re-moisten the entire hand with water when renewing the wiping of the head. Wiping the head is sufficient in any manner as long as it covers at least a quarter of the head. Wiping the ears is easier since it is a Sunnah (recommended act).