Can community users log in from a community other than the custom login page?
Answering the question title, no, community users cannot login via login.salesforce.com or test.salesforce.com. They must login using a community URL. This can point (or be re-directed) to a "standard" community login page (from the template) or a customized one.
With Salesforce, platform users have to have a username that is unique across all Salesforce orgs. However, community users sharing the same username can exist across many communities. It is for this reason that community users can only login using a community login page.