"The shop doesn't open on Sundays."
Translation:La tienda no abre los domingos.
Is "la tienda no está abierta los domingos" incorrect? I know it means "The shop isn't open on Sundays." However, isn't that more or less the same thing?
Although "doesn't open" seems normal in English, it somehow seems as though the store is opening itself (or not) in Spanish. However, I may be mistaken about that.
That doesn't sound correct. That particular construction is called "Pasiva de resultado" because it shows the result of an action, using it to describe a habitual action is not very normal, it would sound normal if you added nunca or siempre.