Does deducting a portion of the money allocated for household needs for the questioner's personal expenses—while counting it as part of the household expenses—constitute a betrayal of trust towards his siblings who contribute to the household expenses without their knowledge? And will he be absolved of responsibility if he informs them after completing his studies?

It is not permissible to take money from your father or brothers without their permission, as that is a betrayal of trust. As long as you are able to earn a living, your father is not obligated to spend on you. What is incumbent upon you is to repent and return the money you took unlawfully, or to seek their absolution. Procrastination in this matter is not permissible.