Is it legal for the village head to set up a property management company privately and it is also wholly owned by a legal person (the legal person is the village head)?

If it is a company established by his personal property, it is of course legal. If the company is established with the funds of the village committee, the shareholder of the sole proprietorship company is only the village head, which is illegal and encroaches on the property of the village collective. If the sole shareholder of the company is the village collective, then the legal representative is of course the village head, which is no problem. Make it clear that a legal person is different from its representative. A legal person is an institution, but its representative must be a person. Shareholders can be organizations or people.