Hey Gideonj,
first of all - welcome! you have come to the right place, and you'll find plenty of information here, and lots of people to answer questions. it is a stressful process, and we all go through phases of ups and downs, so that's normal! welcome to the club....
You don't need to register officially as common-law, if you have been living together for a year, and can prove it, then you are already common-law. You don't need to marry either - at least not for the application, as if you qualify already for common-law, it's pretty much the same proof you will need.
As for outland or inland - outland is way faster! if you check on this page, on the top you can see the difference between outland and inland, and what to consider if you want to be sponsored - you can start by reading that. current times are 90 days to get approved as a sponsor, and on top on that, 7 months for London applicants, but it can also be a lot faster. You can do the outland process even if you are living in Canada, no problem. If you already have a visa (from what I understand) you could start the process now, and maybe your visa will run out before you get the PR approved, but if you are from a visa exempt country, then you can wait in Canada on a visitor visa. You wouldn't be able to work in the gap between your IEC and your PR visa, though.
For your girlfriend to sponsor you - there are no income conditions, unless you have children. so the fact that she is a student is fine. The main thing you will have to prove is that you are returning to Canada ( easy for you as you already live there) and you are in a relationship. She also needs to qualify as a sponsor (check the CIC website to see > criminal check, no bankruptcy etc.).
apart from that - start gathering evidences, proofs of relationship, of living together, download all the forms, and start filling them out! it takes a while, it's a stressful process, but you can always come here for advice, and read what other people have done, how they have organised their application etc, and you will be fine!
Good luck!
Sweden