Is it permissible for an airline employee to purchase tickets cheaper from another agency, then sell them to travelers at a higher price without their knowledge, while offering a price lower than other agencies?

If selling airline tickets is for your own account and not for the company's account, then it is not permissible except under certain conditions: that you do not practice this during working hours, that there is no condition from the company prohibiting it, and that you do not exploit your position in the company to attract customers to yourself at its expense, as this involves a breach of trust.