Work hard! Be sincere and express real interest in what's going on. If asked to work overtime, go for it! And discuss with your mentor and manager that you're really interested in coming on full time after graduation.
If you want a full time offer, make it known that that is your intention immediately and to everyone possible. There are plenty of networking activities including interviewing leadership in other departments, or scheduled networking events. Explore multiple roles. Boeing offers rotational programs as well. Interns apply to these and interview during their internship, and these are typically the first offers given out so I would definitely recommend applying.
3. I was offered a job after my internship for the same role I did over the summer. My manager said that he liked how I was taking initiative by constantly asking for new projects (not just from him but all the other employees in the office), always asking questions when confused, and making relationships within the office. You WILL have downtime and it is important to show that you WANT to be there and learn, not just sit there and burn time. I know it might sound obvious, but you will be surprised how many interns will do just that once completed with their project. There is always something to work on.
Use open communication with your manager sponsor, and let them know what areas you would like to explore for a permanent position. Make note of managers in areas you would like to work and ask them to mentor you.
I spoke to a few managers at Boeing and their consensus was that as a new hire out of college really the only way into the company is through the intern program. At the end of the internship depending on performance interns can be offered leave of absence which essentially means once you graduate you have the option to return to the company if a position is open and available. At the end of my internship I was offered this. Overall an Intern needs to show that they can learn quickly asking questions when required, take on responsibility and ownership of projects, produced quality work, and manage time effectively.