Is it permissible to refuel a car or change its oil at the company's expense when the trip is for the company and with its approval? And is it permissible to lend another car for this purpose?

If the company authorizes filling up with petrol and changing the oil at its expense, there is no harm in that, provided that the company's conditions for its use are adhered to. So, if it prohibits its use outside the scope of its specific work, or only allows it for its own vehicles, then these conditions must be adhered to.