As the others have stated, very few with CIs can use the phone on a regular basis.
I ought to know as I'm one of the few. I attended a CI seminar in January of 2008. They asked who could use a phone pretty well and only 3 out of 50 of us raised our hands. That somewhat surprised me as I have no problems whatsoever using the phone.
To answer your questions...
1) I have the Freedom (Cochlear Inc.)
2) I used the phone two days after being turned on and was pretty much a regular user of them the week after that.
3) No, I have never been dizzy with my CI. On a side note, it has been said that a CI helps those with Menerie's disease.
To keep from being totally discouraging about phones, I have seen several who are occassional users of phones but not on a regular basis.