What version are you running? Have you modified any stock files?
registered users cannot edit thier profile.
Users should always be able to edit their profile, we don't have a permission to deny it; that'd be a "site" permission if there was one as it wouldn't be forum specific. Unless someone went in and edited scripts/editbasic.inc.php and changed it to one of these (default is 0) I'm not sure what's going on:
"admin_only" => 0,
"admin_or_mod" => 0,
user are complaining they cannot include a link with a reply.
Users should always be able to paste a link into their post, the only thing I an think of is they don't have access to post BBCode in that forum which would be the "forum" permission "Can post using Markup/UBBCode" which would stop them from using all BBCode including bold italics etc.
When attempting to fix #2 i would highly advise never enabling HTML posting, you'll be opening yourself up to security issues, this option should only ever be used for admin/mods that can be trusted with it.