Is the intercession used to gain admission to the Education specialization, which was not the first choice, considered taking someone else's place? Is the money earned from this certificate unlawful? Is the gift given to the person who interceded considered bribery?

If your admission through intercession with a lower grade does not deprive those who are more deserving of joining this department, then there is no harm in it for you. However, if it leads to that, then it is not permissible because it is an injustice and an infringement upon the rights of others. To ascertain whether this will result in someone being deprived, you should consult the specialists in the administration of the educational institution. As for the matter of giving a gift to the intercessor, there is no harm in it if their intercession does not result in injustice to anyone, and if their work was not part of their official duties for which they receive a salary.