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Can I study abroad with a non partner university?

The University options that my uni have partnered with are fine, but not quite what I had my heart set on.
I did research into this before applying to my uni, but at the time I decided I would not be doing a year abroad due to health issues so the fact that they did not have the best options didn’t bother me.
Now I’m in a place where I am healthy enough so a semester abroad, and I am again faced with the issue of the choices not being what I want!

I’m currently at the University of Chichester and I want to exchange to the University of Ottawa in Canada. This is not a partner institution of ours.

I’m assuming without the partnership I would be expected to pay full tuition for the semester there?
Can I ask my university to partner with them?
Is there any way at all I can be funded to go there, or do I accept the options available currently and go for one of them?
The offers (in canada, which I am set on) are Thompson Rivers Univeristy and the University of New Brunswick (the latter being my preferred)

Help!