Is it permissible for a government employee to open a commercial business in his father's name, provided that he does not go to the premises during official working hours, and are the profits resulting from this considered unlawful? What is the ruling on "khalu" (key money) and "tadmin" (subleasing), meaning renting the premises to another for a fixed monthly amount?

A Muslim must observe the general laws regulating labor affairs, in obedience to the ruler, as long as these laws achieve a public interest that is Islamically recognized. Violating these laws does not affect the permissibility of the acquired wealth if the commercial activity is permissible. As for the "khulu" (vacation) contract and "tadmin" (guarantee) if what is meant by them is what was mentioned in the question (the worker paying a monthly sum to the owner and the rent of the shop along with guaranteeing the capital), then it is not permissible. This is because it is a lease that involves leasing consumable assets, leads to uncertainty (gharar) and ignorance (jahalah), and is considered a loan that draws benefit, and every loan that draws benefit is forbidden.