What is the ruling on my action after interrupting my ablution due to running out of water and my family's talking, and my saying aloud that I do not want to perform ablution or prayer? And is repentance obligatory for me, and how should it be done?

The words mentioned are a great error and show severe harshness, for they contain an explicit declaration of not wanting to perform ablution (wudu') and prayer (salat), and defiance towards the father and raising one's voice at him. However, this is not considered apostasy (riddah) unless one intended to deny their obligation, especially if the cause was intense anger and obsessive thoughts (waswas) about ablution. You have done well by seeking forgiveness (istighfar) and praying. You must adhere to proper conduct with Allah and with your father, and not return to such words. Adding to what the Sharia has stipulated for ablution is a prohibited transgression.