Does my brother's reading of a program's terms and conditions suffice for my own reading of them, and what is the ruling on doubting whether a specific page of the terms and conditions was read?

If you appoint your brother to read and accept the contract, or if he reads the conditions and informs you of them, and you accept without re-reading, then that is sufficient. Your doubt about not reading a page of the conditions does not affect the validity as long as you have accepted them. However, one should not sign a contract whose contents are unknown, because it may include the acceptance of something that cannot be fulfilled, or a prohibited condition.