BuddyPress.org

hi
For your first question, you may want to try this plugin
https://wordpress.org/extend/plugins/bp-registration-options/
checkout this thread too
https://buddypress.org/community/groups/how-to-and-troubleshooting/forum/topic/moderate-members/

For the second, yes, It is possible. Just go to SiteAdmin->Options and select the radio box which says only logged in users can create blog.
PHp5 may be an issue, better why not ask your server adminstrator to upgrade.