Many have stood at this crossroad with these questions relying less on scholarship, and the probes into the mystical teachings of this walk, and more on other's thoughts on the subjects you raised.
Your first question: "Baptism. Does it mean the Holy Spirit comes into a person automatically?" Your second question suffers with the first question in a tangle of dogma from various sects in Protestantism: "I thought confessing Jesus, as one's Lord and Savior, meant one was born again?" The last question you ask has the embracing fragrance of innocence and honesty. "So how can you get baptized and not get the gift of the Spirit, that I flat out don't get because the Holy Ghost is a gift after all your sins have been washed away through the blood. I thought a gift is just what it is: a gift!"
My first inclination is to suggest you begin your study, in the Bible, accepting that it is a long process delving into this subject matter. Because the question is fundamental to Christianity. The answers should be more than passable understanding of its progenitor religion, and that worldview needs to be learned to have depth as a follower of these teachings! It is important to have depth with substance, and breaking the tradition of glib answers to profound questions follow Paul's admonishment to "Study to show yourself approved..." and follow suit with your own spiritual practice!
In easier language, there is a nest from which the answers to your questions flew away from! From animal sacrifices to the quest in the first century Church to rid itself of the vestiges of its Hebrew roots, to the horrible centuries of blood conquest/missionary work, to the 20th century revivals until now; the answers to your questions have been altered by histories of actions, politics, and the business of slave trade maintenance. So, your answers are easily assessable in the Bible, but do you really want to explore the fundamentals of your religious belief, or do you simply want to be sure of your salvation?
To honor the questions, I am obligated to honor the teaching style of the Rabbi Jesus, who was initiated into his role, into manhood. He comes from not what passes today as a way into the kingdom of God, but from a tradition steeped in probes into the Unknown, with the tradition of study and introspection of their holy books and rituals interlinked with the development of the abstract and the intellect simultaneously! - Gregory E. Woods, Keeper of Stories 9/18/17