Is it permissible for a Muslim engineer to construct a salon (hairdresser's) suitable for both men and women, knowing that the salon owners are not religiously observant and allow intermingling in their other branches? And is this considered cooperation in sin and aggression?

There is no sharia impediment to establishing and furnishing a salon, even if indecencies occur in it later, as long as the founder did not intend these indecencies and did not directly commit them. The basic ruling for cosmetic work and the mixing of genders is permissible if temptation is avoided and sharia is observed.