Canada sucks for mobile if it hasn't changed much in the 3 years since I was last there, PAYG is much more hassle than it is in the UK and the length of time your voucher is valid for is in direct proportion to its cost usually. Oh and they even seemed to be quite a way behind on the phones you could get on contract plus the contracts were for 3 years at a time if memory serves.
As for bank accounts, I got one from the Royal Bank of Canada pretty easily, I would have had my passport at the time but as far as I recall they were happy for me to have a temporary address and use that although from memory the functionality of the account was slightly limited because of that. Another example of the oddities of Canadian services here though is that banks don't tend to open at the weekend or at least I didn't find one that did - I've discovered that in London now as well though they often don't, weirdos.
Good luck with the move, as mentioned it can take a very long time to get your visa unfortunately.
The comment about phones is certainly true.
When I first arrived out there I had a Sony Ericsson P800 which decided to die on me. So I bought a pay-as-you-go to replace it, and the best phones that Rogers Wireless sold were very basic chunky Nokia's with basic two tone colour screens. It was the kind of thing the UK had years before... but it probably is indicative of the UK culture of people constantly buying new phones.
I had a bank about with RBC as well, however most of the banks charge you for making cash withdrawls. You can also pay a fee each month, in a tier system based on how many withdrawls you think you make, and you only pay the set fee instead.
One of my Canadian friends said one of the best banks was 'President's Choice' which I believe is a Supermarket, and they don't charge for withdrawls... or didn't a few years ago.
I'd certainly think that the OP is overly optimistic about the chances of getting into Canada that quickly. I looked into staying when my one year work visa expired, and it's a very difficult country to get into. No offense to you, but a relationship that isn't very long, based around having met online will come under major scrutiny. Just for instance, have you seen any of those shows on UK immigration, you can see just how much they grill people doing similar things trying to get into this country.
A friend of mine developed a relationship with a Canadian girl during his one year Visa too. After returning to the UK, he made a number of trips back out to her, using the standard tourist (6 months) visa each time. He was eventually told off for this, and warned not to do it again, as he would likely be refused entry to the country.
Another couple I know ran a holiday/accommodation business, UK based, but they moved to Canada, so it was technically legal for them to do so. However they only had tourist visas, but their daughter was born in Canada, meaning she had dual citizenship, so their application for residency was based on that. Unfortunately though, the Canadian government didn't like that, and so they had to move back to Europe instead.
As others have pointed out, it takes years to get a Visa, so as much as you might like to see her often, your at risk by making lots of long trips without working. If you dare overstay a tourist visa you will be shooting yourself in the foot also.
Good luck though, it's such a great country.
