I would check out http://docs.elgg.org/wiki/Themes
For your requirements #1 and #2 you need an elgg theme. There are plenty of Elgg themes available here in the community. Download one and digg into the code. The link Evan posted explains well on how to start with theme development.
Try using anirupdutta facebook login: http://community.elgg.org/pg/plugins/project/733084/developer/anirupdutta/facebook-a
It is for elgg 1.8
Rodolfo Hernandez
Arvixe/Elgg Community Liaison
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