1) Am I still considered a resident of Canada? I'm from Ontario and go back to my Canadian residence, which is my parents' place, every couple months. So do I claim NRA or RA for US tax purposes?
It's up to you really, there is a complicated calculation under the tax treaty but essentially if you want to be a resident of the US for tax purposes you can, if you want to be a resident of Canada you can, just means you have ties to one country or the other usually (DL, healthcare, etc.) Generally what I recommend is that if you're spending less than a full calendar year in the US (i.e. Jan-Dec) then it's not worth the effort of moving your tax home from one country to the other and the CRA and IRS might not believe you anyway.
2) Will I have to pay
taxes to both governments from my income? What procedure must I go through in order to ensure I'm filing correctly? or could someone at least tell me how and/ or where I can find this information?
IRS publication 519 - but be aware of the fact that the tax treaty between the US and Canada is very comprehensive and eliminates a lot of the things 519 talks about, like non-resident alien tax.
If you move your tax home to the US, you file a pro-rated T1 for this year, and file dual-status in the US. If you keep your tax home in Canada, you file a T1 as normal and a 1040NR in the US. You claim a foreign tax credit using forms T2209 and T2036 so you don't get taxed twice. The T1 general guide explains how to do this.
If your income is over $100,000 then the IRS may want you to file an 8833 with your 1040NR if you do it that way. I have no idea how to fill in that form!
Usually people move their tax home to the US because the taxes there are lower, it's a good idea to sit down and actually work it out using both methods, resident and non-resident and then you can make an informed decision. For example you may say to yourself that you're staying for 2 years but you're paying more tax doing it that way - but it's not worth the hassle of moving your tax home so it saves cutting all your ties to Canada.
Also be aware of the fact (which IRS publication 519 will bring home to you) that moving your tax home back to Canada later on is a bit of a pig, lots of forms you potentially have to file, they're all listed in there.
Steve.