What is the ruling on inviting someone to a feast or giving them a gift in exchange for hiring them for a job, and what is the ruling on the money they will subsequently earn from this job?

There is no sin in holding a banquet, giving a gift, or paying money to obtain a job if it is lawful, you are qualified for it, and it cannot be obtained otherwise. The money earned from this job is halal if the aforementioned conditions are met.