1) No
2) For global rights (aka to assign rights to all projects) you can create groups like "Mantis Admin", "Mantis Developer", etc within Geeklog. This is currently an undocumented feature. You can get more info on the group names you must use by looking at the code in core/user_api.php.
3) First you can set global default access by editing the config_inc.php file. This is delivered as REPORTER (see the following code):
Text Formatted Code
$g_user_default_level = REPORTER;
As an admin or project maintainer you can go to "Manage Projects" page and assign users rights to particular projects. This overrides the global rights they have (unless they are a global admin).
-Vinny