Does facebook have a public search API yet?

You can use the Facebook graph API :

http://developers.facebook.com/docs/reference/api/

look for the searching section,

QUOTE from fb:

Searching

You can search over all public objects in the social graph with https://graph.facebook.com/search. The format is:

https://graph.facebook.com/search?q=QUERY&type=OBJECT_TYPE We support search for the following types of objects:

All public posts: https://graph.facebook.com/search?q=watermelon&type=post

• People: https://graph.facebook.com/search?q=mark&type=user
• Pages: https://graph.facebook.com/search?q=platform&type=page
• Events: https://graph.facebook.com/search?q=conference&type=event
• Groups: https://graph.facebook.com/search?q=programming&type=group
• Places: https://graph.facebook.com/search?q=coffee&type=place&center=37.76,122.427&distance=1000
• Checkins: https://graph.facebook.com/search?type=checkin

You can also search an individual user's News Feed, restricted to that user's friends, by adding a q argument to the home connection URL:

• News Feed: answered 2011-02-26T10:13:06.363