Yes, возглавить = to become head of.

1. The new development company is responsible for the building and maintenance of the road. - За строительство и ремонт дороги отвечает новая строительная компания.
2. His wife is responsible for the payment of the interest of the loan. - За выплату процентов по займу отвечает его жена.
3. They left here responsible of their dog while they will be abroad. - needs clarification, or mistake
4. He is not a responsible parent. He left his child waiting him one hour outside of the school. - Он безответственный родитель. Он оставил ребенка на целый час ждать около школы.