P2 Theme by http://automattic.com/ does that and it is a wordpress theme.
It has been running on my blog ( otsotm.com ) for couple months now.
As soon has i post something, i see the post pop on the other main page of my blog i had open.
To fix the Facebook connector should be relatively easy - that and AjaxedWP are most likely defining the same variable so causing issues.
The removing of #awp would most easily be done by using mod re-write rules of Apache which you can set through .htaccess
For the shuffle/random to work, you will probably have to define random with a JS random number generator.
As for the others, I am by no means an expert in ajax (and have never used that plugin) but...
You should be able to define how long the slides takes and height offsets as the whole plugin is using the MooTools framework and there are a bunch of examples over at http://mootools.net/ to look at.
It looks like you're new here. If you want to get involved, click one of these buttons!