The first time I ever heard anyone say "tore" when they mean "tour", which I am used to hearing as "toor", was in the movie "Tin Cup" when a sports announcer pronounces it that way. Since then, I have heard it fairly often in the media.
Yes. That's the pronunciation I first learned, in a small town in New York, then changed it when I started to learn French in fourth grade.
Websters gives several pronunciations, including reference to the one with two syllables I was about to mention: too-er.
tour
They all sound fine to me.
This may be a north-south division. I first started drinking Coors beer in Oklahoma. When I moved to Kansas, I found more Cores than Coors.
There's another highly specific pronunciation of tour: Tower, as in Eiffel. Bus drivers refer to their morning and evening shifts as Towers.... but the overnight shift is the Night Train, not the Night Tower.
As a British English-speaker, I find this interesting. To me, there is no difference in pronunciation between tore and toor! (To give an example of actual words, in British English the words more and moor are pronounced the same.) In Britain, we pronounce tour pretty much as the French tour (as in Tour Eiffel) or, as has also been mentioned, as too-er (but as one syllable, if that makes sense).