That's the correct order of events, yes.
You'll see it as a regular post request, but there is an extra header of "X-MicrosoftAjax: Delta=true".
It's not comprehensive, but this post might help a little with the events: http://encosia.com/2007/10/24/are-you-making-these-3-common-aspnet-ajax-mistakes/
To do that, you'd want to set the dropdown to autopostback. Then, add the dropdown as an AsyncPostbackTrigger in UpdatePanel2's Triggers collection. In your Dropdown_OnSelectedIndexChanged handler, if you update the label in UpdatePanel2, the update will automatically be displayed.
These video tutorials might be helpful: http://www.asp.net/learn/ajax-videos/