Start here:

http://moz.com/beginners-guide-to-seo

http://moz.com/blog/how-to-rank

These will give you tons of help in how to start ranking keywords.

Once you understand and implement this research/ideas/concepts.

THEN, keep track of what is working and do more of that.

Videos are pretty new to Facebook.

We also know that Facebook does NOT show everything to all people, even if you engage and follow a page.

There is some sort of algo that hides posts and only shows to certain fans.

I would say that Facebook is deliberately throttling back on the videos more than regular posts.

This is an answer about Tumblr posts not showing up, and the answer might apply to Youtube as well.

http://webapps.stackexchange.com/questions/28208/tumblr-items-published-from-queue-do-not-show-in-facebook-timeline-only-those

Facebook wants to keep the "facebook content" and is hiding linked content.