I think I used the same installation kit on my truck for a Single DIN. I seem to recall a similar issue, but needing to remove one of the two "snaps" on both sides of the "pocket". I found it easier to install the bracket with the sheet metal sleeve to the radio bezel, then slide in the head unit til she clicks. Then install the radio bezel with the radio. Don't know if it's improper, but I haven't had the radio fly out in the 7+ years or so since installation of two radios. Now when I remove the bezel, the radio comes with it 'cause it's easier. Thank goodness for wire slack!
No, you do not remove the factory rail. You should attach the supplied bracket to the back of the radio to support the rear of the radio. It can be kind of a pain to locate it at the correct height though. You can get it really close comparing it to your stock radio.
Is this the one?
Link: Metra Online - 99-5027