Do you mean "Merritt" is one of your Easyocial group?

1. This group needs to be the only ones that can add posts to a particular blog category and subcategories.

Unfortunately that is not possible to achieve this at this point of time.

2. To have a separate custom login/registration page for people wanting to register to this group.
...preferably redirecting a separate page from regular login/registration.

Do you mean when someone wanted to join this group "Merritt" then you would like to redirect user to register to particular profile type?

If that is the case, currently that is no such of setting can configure this, it required to have some of the customization into Easysocial core file.

If you really want to achieve this on your site, you can always request for a quote from us at https://crm.stackideas.com and select "Customizations" . Our sales person would gladly send you a quote for the customization that you have requested.