This is a fascinating thread, because back in 2015 I went through all of this myself trying to figure it all out. PhD student in the US, but Canadian citizen (and factual resident).
@TakeruK, I'm wondering if you had the same experience as me on one thing. When filing with the CRA, I found the foreign tax credits (i.e. deducting the amount I pay in US taxes from my owed Canadian taxes) to be useless. Unfortunately, tuition credits are applied before foreign tax credits are, so my tax was reduced to 0 due to my tuition credits (about US$50k), and therefore there was nothing to apply the foreign tax credits to. This was quite saddening because it meant I paid taxes in the US but ALSO had to use up my tuition credits in Canada. Does this sound familiar to you, or did you find some sort of workaround for that?
One topic I saw a lot earlier in this thread was that grad student assistantships aren't considered taxable by the CRA (and there was some back-and-forth on this). I thought I might provide some clarity on the official stance on this. Here's the relevant document: Folio S1-F2-C3. Look under the "Student Assistantships" section:
"As a condition of receiving financial assistance, a student (usually a graduate student or an upper-year undergraduate) may agree to do some teaching, marking of examination papers, demonstration of work, or research as a member of the staff of a university. If part of the assistance is paid in the form of a fellowship (for doctoral as opposed to post-doctoral studies) and the remainder as remuneration for the performance of the duties, those two parts are treated differently for tax purposes. The amount received as a fellowship is subject to subparagraph 56(1)(n)(i), while the amount received for services rendered as an employee is considered employment income under subsection 5(1)."
In my experience, everything in the US that is termed an "Assistantship" (whether a Teaching Assistantship or Research Assistantship) has at least some condition on something the student must do for the university, even if it's just that your advisor specifies which research project you work on (the one funding the RA), otherwise they will call it a "fellowship." Therefore, these payments should almost certainly be reported as taxable income in Canada.
EDIT:
In further reading of that linked Folio, there's a specific section for "Research Assistants". Basically, it says that if you're paid as a student doing research with guidance from a professor, and that funding comes from a research grant, then it is considered to be a research grant for the purposes of your income tax. A bit above that is a section that describes how research grants are taxed, which is basically that anything above the costs of the program you're enrolled in are considered taxable income. So, if you pay tuition of $40,000 and get a $50,000 research assistantship (but no tuition waiver), then you claim $10,000 as taxable income. If you pay tuition of $40,000 with a full tuition waiver and get a $50,000 research assistantship, then you claim all $50,000 as taxable income. I think.
