Login block & Me

I have an option "Rewrite links generated by the drupal menu system" checked (selected), and "Redirect to uid" unchecked (unselected). I prefer that users always just see and use me instead of being concerned about their uid (I believe these settings should ensure that).

I have a problem with Login block (I don't use menu item for user settings and/or login, just this block to login / logout / edit user):
1. As soon as I am on the /user/me pages, Login block is not visible / present (I have an option "Use me alias on every path except the listed paths." selected, and no paths on the list below); this block works well if I am accessing those pages through /user/uid...
2. When the Login block is visible (I believe all other pages but /user/me), a link to the user settings (within a Login block) is not rewritten (it links to /user/uid instead of /user/me)

Within user settings pages, everything is rewritten just fine.