Computer tools can definitely help, however, you should understand HOW to graph a function manually, since that's a check on whether you understand the material. This sort of thing is usually covered early on in your study of calculus. I suggest you do it until doing so further would become tedious and get in the way of learning new things.
When I work through math books, I usually work out the problem with a pen and paper, and then I typeset them on a computer. This is useful so that I have something legible to go back and read if I need to, and I also have a terrible habit of picking up a random notebook and selecting the first nonblank page I find.
As for the problems, do as many as possible, and try to think why the author included each particular question, what was it trying to teach? If the author follows good pedagogy, often solutions to subsequent problems stem from concepts unlocked in prior ones. If you must skip a problem, make sure you at least read through it, and work out how you'd approach it. If you fail to solve a later problem, that's probably a good sign that you need to revisit an earlier one.
It took me a long time to realize it, but the problems in a math book are the most important part. Since I learned most math by self-studying, while I dutifully read every theorem and went through each of the author's proofs, I initially I skipped all the questions, dismissing them as busy work for students in courses. Terrible idea, because I didn't even realize what I didn't understand! For some reason we are able to learn, and recall concepts much better after we have worked through them ourselves. Reading a math book like a novel is a good way to forget all the content!