Is taking a job through wasta (mediation/connections) without paying money, and only succeeding in the language test, forbidden? And is the salary resulting from this job forbidden?

If the husband is proficient in his job and performs it as required, then there is no harm in the salary he receives, even if he succeeded in the job test through cheating. However, he and his relative who assisted him in the sin must repent to Allah for the cheating.