Yes you could drive across Canada I did myself before
I would contact Budget directly. I have done exactly as you are asking, but was required to specify that I intended to cross the border and had to sign additional documents.
In Canada we do the reverse all the time for trips to the US. Up here they always ask if you plan to cross any border, but it's for insurance and customer service reasons (which to call if you break down)
Yes but you need to chech the insurance provisions specifically. This will be relatively normal if you are renting from a location near the border. You should clarify if you intend to cross the border and then return, or return the car in Canada.
Sure, but so expensive.
It would be best to contact Budget Rental directly.
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