I have no input on undergraduate admissions. Yes, by all means. Give us a call a week or so ahead of time, and we'll try to make certain you get a tour. The freshman introductory course, AAE190, has four hands-on engineering design projects, plus tours of many laboratory facilities in the department. Yes, if you have the standard curriculum well in-hand.
Opportunities come and go depending on research load, lab and equipment availability, etc.
Purdue and the department have numerous public terminals, workstations, and PCs available on campus. Everyone's needs and resources are so different, making this a very difficult question to give a simple answer to. Students go through here with high marks without every owning a computer. Others own a computer. Engineering studies at Purdue or any other leading university are four years of work to prepare you for a forty-year career.