Hi Alex,
I am really sorry for the delay of this reply. Please find my answers from your inquiry below.
How can a post be deleted?
You need to allow certain profile types to be able to delete stream item by going into your backend > easysocial > profile types > ACL > stream,
http://screencast.com/t/uV7hKVTZN . If set to "Yes", user will be able to delete their own stream item from frontend.
And why can't all posts be edited?
This is to avoid unnecessary issue with stream formatting when a user decide to edit a stream item such as photo stream into a different stream such as status update only.
Are these features available on the new update? I haven't installed it yet.
Easysocial 1.4 has the same behavior as easysocial 1.3 where it will not allow certain stream item to be edited such as photo stream.