You can't 'submit' an incomplete application. If you're submitting it to a university, you have to have everything completed - this means your personal statement, your reference, etc. If you're going to apply to another university in addition to Oxford however, I've read here that it's a good idea to send the others off separately, to give you more time to think, and so they won't suspect you're an Oxford applicant.
It is expensive to travel, but... I personally wouldn't mind the trip and it will be worth your money if you
do make it (get accepted, I mean). I know that a Canadian passport is quite literally a 'passport' to get in hassle-free to many countries... not so sure about the US, but in any case it shouldn't be an issue visa-wise. They would really
prefer you to come in-person.
I know a lot of (all?) applicants from India have a phone or Skype interview... As to how it's harder to get in... well, they really can't judge you well over a camera and a microphone.
Re: Assessments. I have to take the TSA, and I've read about how admissions tutors view the scores. I don't know the 'weightings', but in general... if you get an average score (oversimplifying it, but ~60%) they will think you are 'suitable'. If you get a good score (~80%), they will factor this into your application and choose you even if your personal statement/grades aren't amazing. If you do poorly, well they'll know that you got your grades by some fluke, and really aren't suitable for that particular course.
Hope I helped.
ETA: On the admissions test site (
http://www.admissionstests.cambridgeassessment.org.uk/adt/) they have graphs of results from last year. Click through and view them.
Just to get a general idea of where you're heading... do you have any particular area you're interested in going into? Humanities, Languages, etc. ?