Is the salary resulting from a job obtained through wāsiṭa (mediation/favoritism) permissible or forbidden, and is it permissible to use the experience gained from it to obtain another job?

Obtaining a job through mediation is an infringement upon the rights of others. However, the salary from this job is lawful if you perform your duties as required. If you are unqualified and unable to properly execute the assigned tasks, then remaining in that position is harmful and a betrayal of trust.