I'm from a programming background and I recently started reading on category-theory and as of now, my understanding of what a is category is they are just objects that are connected to other another by arrows or, from where i read it, morphisms. Please correct me if i got it wrong.
My question is if the order of the arrows or morphisms are meaningful? If I swap them around, would it still be valid?
The order of the arrows is important. In all the basic examples of categories, the objects are some kind of set with addition structure, like groups or rings or modules, and the morphisms are functions that preserve that structure, like group homomorphisms, ring homomorphisms, or module homomorphisms. Functions care very much about which direction they are pointing, so yes, the order of the arrow matters.
Nevertheless, there is a very important category theory construction in which you form a new category from an old one by reversing all of the arrows. This new category is called the dual category. See https://en.wikipedia.org/wiki/Dual_(category_theory).