What branch of government establishes post office and roads

It's the Congress who establishes post offices and roads

The United States Congress is the department that establishes the post office and roads. Congress was granted the power to manage the post office and the transport network, by the Articles of Confederation. The reason why the road network is part of the Postal Service is because originally the roads were created to facilitate the transport of the post to various outlying areas in the USA. It is fascinating to realize how important it was to deliver the post to its destination.