Is it possible to use the VIM component as the editor in KILE instead of the integrated editor? ...some of us are just used to VIM :)
...it seems that in parts of KDE it is easy to use VIM over standard Kate.
...sorry if I missed this point in the doc, but I could not find it.
No, it is not possible. Btw, the KVim is part is not fully implemented, so even if it was possible you could not use all the features in Kile.
Maybe you can use yzis (http://www.yzis.org/) as a replacement. Milestone 3 (M3) is out and is already quite usable. It is not yet 100% VIM compatible, but the feeling is there.
I would recommend the Vim-Latex Suite. Though less user friendlily than Kile, you may be more used to it :)