Re: Can we run just the repository without Alfresco share or community?
Yes, you can only use the Alfresco Repsoitory (alfresco.war) as a backend to your applications. This is the use case of Content Services.
There are no separated packages for users, repository etc. the repository is one complete application. Alfresco is currently in the process of shifting some parts of their applications more to a micro-service oriented approach, but this is primarily to make the whole application simpler to scale, and not necessarily to make more components / packages optional.