What a great question - I wish I had this site when I was negotiating my own internship->full time transition, or that I could have pointed my old beloved interns to it as we did the same thing! I've been on both sides of this one.
First - most smart companies regard good interns as one of their best recruitment streams. You can never really get enough of them - it takes time and commitment to mentor an intern and not every intern works out to be a good candidate for full time employment, but when you are a hiring manager you know so much more about the qualities of a former intern that you can feel many times more certain about hiring them. Beyond internal business knowledge - the knowing what you're getting quality is really the best part of the process.
And that's true for both sides - as an intern, you know what you are in for, too.
In general, a job application and offer process is (and should be!) formulaic to some extent. Likely, it will appear more formulaic than it actually is. In a big company there is an outlined process to the application/interview/offer process that is created by HR and legal to be sure that candidates are treated fairly and compliance with company policies - it should always be on the merits of the candidate and nothing sneaky. So being asked to submit an application, go through a round of interviews, and being handed an offer by someone in HR who you may never have met before - may all be typical.
What isn't usually obvious is that for a known-to-be-excellent Intern, the hiring manager and the former managers of that intern have a lot more to say on the back end. Somewhere in the back of any bureaucracy are some real people trying to make honest decisions. Likely some of these are managers who know you and who are basing their decisions on your hard work. They may, or may not, be the ones asking you to apply, or talking you through the process - it depends on company rules.
Even for an unknown guy of the street a person with project and budget control eventually has to make that salary decision - HR may advise, but someone with business knowledge is usually the final yes/no guy.
s salary for an internship -> fulltime offer with larger companies a process which is normally "automated" from a company perspective in that there is a "for this education and degree, here's the offer" format? IE a formulaic offer process instead of a customized, individual offer for each intern->fulltime position. Or should I treat it the same as if I had recently interviewed?
Some formalization will happen, but you can expect some degree of bias based on previous experience with your skills. For certain types of jobs (usually government) they may be handicapped by rules and regulations - such as X degree starts and entry level job at Y value. In other cases, there are likely limitations of "we are not paying this guy dramatically more than the other 3 guys who do the same job already". And always - "we will not pay this guy more to do this job if we can hire another guy to do the same job for radically cheaper".
2.Can I consider my 2-3 years of internship and graduate research as work experience for a request for higher salary - even though I will technically be graduating?
Yes. Usually graduate work and internship experience count as work experience. They may or may not qualify you for a higher rank, but they do factor in.
Also - check with your company - you may count these years in seniority calculations - factoring into your earned vacation time and other perks.
3.Is discussing previous (positive) performance reviews an acceptable part of a fulltime offer negotiation?
This is usually a part of an interview process. Discussing specifics of work as part of salary negotiation is (in general) a bit too nitty gritty.
4.Is something like, "I would like to work in this position, however, other jobs I am qualified for make $XX,XXX and this offer is only for $YY,YYY, is it possible we can meet in the middle?" acceptable?
Know your value - have another job offer in hand if you want to have this conversation. I wouldn't offer a compromise - I'd start with what you know you can make elsewhere and see where they go with it. Sometimes less is more.
Rarely have I seen a company WITHDRAW an offer because the candidate counter offered. Several times I've seen the answer be "nope, take it or leave it". So realistic worst case is no change.
Keep in mind - they know you, this cuts both ways. They know what you can do... and what you can't... you may be terrific, but you can't clone yourself, so you aren't going to pull off double the going salary.
5.Finally, if an offer details are communicated primarily in email format, should I attempt negotiations over email or via phone?
Depends. I'd follow the lead of your communication channel.