Is it permissible to use money designated for internet access for studies for other matters, such as reading fatwas? And is this considered a gift that necessitates fairness among siblings?

There is no objection to a father designating one of his children for university study expenses without including the rest of his siblings, as justice is required in a pure gift, not in expenditure.

As for using the Internet for purposes other than study, the principle is to adhere to what the father has commanded or to the purpose for which the money was given. The prohibition is confirmed if using it for non-study purposes reduces the minutes available for study. If a father gives money for a specific purpose, it is imperative to use it for that purpose, out of consideration for the father's intent, unless his words were merely a common casual remark.