Hi Creative Overflow,
first off I should say that I'm just going through this process myself, and there are definitely people on this board who will be able to help you more than me - but I think I can answer some of your questions.
1. You could get a letter from your parents stating that you've been living there X amount of time, signed by them and yourselves, and notarized... that should function the same way a lease from someone else would - maybe even better, since it shows that your family supports your relationship.
2. From what I can tell on this board and others, conjugal relationships have a very high rate of refusal as compared to your other options. IF (IF!) you can get your application together before her current visa expires, and it is received before same, you can include an extension of stay application in the SAME ENVELOPE as the sponsorship app (you can even check "open work permit" on this form, and once you get to first-stage approval, she should receive this permit (it's called "Acceptance in Principle". The processing times inland (processed in Canada) are 11.5-13.5 months right now. Downside: she shouldn't (read: REALLY shouldn't) leave Canada during the time the application is being processed - if she is denied entry for any reason, she won't be able to attend her landing interview and will forfeit the application. If you went this route, you could apply as commonlaw.
You could apply from outland as well - but that would mean (i think - someone else may be able to clarify better than I) a conjugal application, which, from what I hear, would require a huge amount of proof. The processing time in Japan is currently an average of 6-7 months (plus 1.5 months for the sponsorship part). Lots faster, but maybe harder to prove, and unless you can accompany her, you'd have to be separated during this time, as it's unlikely they'll allow her into Canada again during the process.
for examples of proof you could provide with your application, you can check what I've included at
http://www.canadavisa.com/canada-immigration-discussion-board/final-draft-opinions-t23568.0.html - people who know much more than I are telling me this is a strong application.
from what I can gather, the consensus around here is that if you're a reasonably prudent and organized person, an immigration lawyer is basically a waste of your money, and there's no reason you can't do this all on your own. EVERY CASE IS DIFFERENT though and it may be beneficial to yours - not really sure.
I hope some of this is helpful to you! I want to restate that I am NOT an expert on this stuff, just someone who's done his homework, and the other folks on this board (for example, robsluv, boncuk, PMM, leon, MARLENA, and others) know a LOT more than I do, so please seek their opinions before following my advice.
Best of luck to you!!!!!!!!!