1 .well the issue is with the login link , you are using own custom link to login into wordpress and also using that link to logout the user form wordpress but here is the issue is appearing , when you log in through wp login or some login widget it logs user into the vibebp but it does not log user out on your custom logout link .
So you need to add our header which have our login/logout .
2 . Yes this is actually an issue , we have fixed this and fix will be available in next update of vibebp plugin .
3 . try adding this custom css in your wp-admin-> appearance -> customize -> custom css :
.profile.public.buddypress .widget.buddypress.widget{
margin:0 !important;
}
.profile.public.buddypress #bp_core_whos_online_widget-3{top:0 !important;}
4 . YEs this is happening , we will try to fix it but its highly unlikely user will scroll while being the mobile menu opened.