Only to outsiders because individual states do not make treaties with foreign countries. However states do sometimes send their own commercial ambassadors and meet with world leaders.
States also retain full sovereignty of their territory except for limited cases and maintain their own armies navies and air forces
The National Guard are the individual armies of each state. Typically, they aide the army and obey national orders. However their commander in chief is the governor of their state not the president.
As an example, California has pretty strict border controls on its state bordera. Bringing certain agricultural goods into california is illegal and they will fine or jail you depending on the severity.
It is entirely possible and legal, but unlikely, that the governor of California sends it national guard troops to the border if Oregonians for example were attempting to storm the border with ferrets or something.
States also retain full sovereignty of their territory except for limited cases and maintain their own armies navies and air forces