Is it permissible not to adhere to the 30% agreed upon with the sponsor, and to give him only a quarter of the amount? And what is the jurisprudential ruling on the sponsor taking a percentage without providing work?

Islam encourages the use of status and influence to help others, as the Prophet, peace and blessings be upon him, said: "Intercede, and you will be rewarded." This is permissible in exchange for a benefit if that benefit is for a service rightfully due, such as visa and residency fees. Therefore, you are not required to pay anything to your sponsor unless it is in return for an effort for which they deserve compensation.