Drupal login using other subdomain user account with certain role I'm having a main site and few subdomain sites for different countries:  


www.mydomain.com (for U.S users)
newzealand.mydomain.com   
singapore.mydomain.com  
australia.mydomain.com


For each site, there are roles of anonymous user, authenticated user, member.
Rules module is used to add "member" role if this is an active user, and remove "member" role if this is not an active user.

I'm going to have another subdomain, members.mydomain.com.  

Only those users with "member" role in those subdomains are able to access to members.mydomain.com.

In members.mydomain.com, how am I going to retrieve the user login info and user role from different subdomain?
Are you using different databases for all sites? or the Domain Access module? https://www.drupal.org/project/domain

If you are using different databases for each site and if they are on the same server I would consider to let the sites share the users + users_roles table. 
In that way all users exist on all of the sites with the same password and have the same role everywhere. You can then assign different permissions to different roles per site.