1. Debian is moving to libreoffice as are ubuntu, fedora, and just about everyone else. The problem is that Oracle brought out Sun, who were the previous developers of open office. Unfortunately Oracle seem to have zero interest in free open source software so Open Office has been forked by a group of open source developers. The fork is called LibreOffice.
2. At present there are no differences apart from the branding. Open Office is a trademark owned by Oracle.
3. Libre office for the single reason that it is free open source software driven by community development. Open Office will probably die a slow and horrible death with Oracle behind the wheel. Those guys only care about one thing - profit.