An argument is only one of many kinds of written or spoken thought-products, and logic focuses on evaluating arguments. Thus the connection between logic and thinking is rather indirect. Before long you will encounter some rules or guidelines for how to evaluate arguments, but they will not be rules for what your inner thought processes should be like. Probably studying logic will have some beneficial effect on your thought processes, but that is not the major focus of logic. It's a fringe benefit.
Every argument has a conclusion and it also has at least one reason, maybe more.
So it takes a minimum of two statements to make an argument. The definition implies that every argument is a group of statements, but it does not imply that every group of statements is an argument. When this happens, which is very frequently, the result is a group of statements that is not an argument. There is nothing in the definition about debating, disputing, or disagreeing. An argument need not involve more than one person.