I'll try an answer those questions for you.
1 : Admins & Mods can move images in bulk, but if you enable a user to edit a photo (all done via the photopost usergroup manager) a user could move an image to another category, but only one at a time.
2 : To allow HTML for a description isn't possible within the normal running of photopost, but concider that enabling HTML 'could' compromise your server if a user posted some malicious code, i think checking over at photopostdev.com
you may find a hack for this.
3 : You could try editing the templates (showgallery for example) but remember this would be a global edit and thus all categories would be 'linkless'
4 : Achive this by simply editing your usergroup permissions and also by editing category permissions.