Is it permissible for a scholar or a student of knowledge to transmit a religious ruling that they are certain of without mentioning the evidence, while reserving the right for the recipient to request the evidence, or is that not permissible except by always mentioning the evidence?

It is not permissible for anyone to issue religious rulings (fatwa) except for one who is knowledgeable of the Sharia. The mufti (issuer of fatwa) is not required to mention the evidence to the questioner, especially if the evidence requires ijtihad (independent reasoning) that an ordinary person would not understand. As for taqleed (following a qualified scholar), the principle is to follow the evidence for those who have the ability to differentiate between proofs. For those who do not possess this ability, it is permissible for them to follow a knowledgeable scholar whom they trust. The questioner should debate in the best manner and avoid disputation.