Welcome to Meta 
This is the topic about the beta phase. Since then, the free plan has been officially released (see: Introducing the Discourse Free Plan) and has kind of replaced the Starter plan. You can see the limits of the free plan on the pricing page. I don’t want to copy the whole table, but here is the beginning, where you can see, for example, the limits for page views, emails, and categories.
Yes, you can choose the name of the categories you create.
The default groups in Discourse are a staff group, where both users with moderator status and users with admin status are. Additionally, there are 2 separate groups for these roles.
There are also default groups containing the users with each trust level and up: trust_level_0 for TL0 and up, trust_level_1 for TL1 and up, trust_level_3 for TL3 and up, and trust_level_4 for TL4 and up.
There are also pseudo-groups for logged_in_users, anonymous_users (those who are not logged in), and everyone (which includes both prior mentioned groups, but is probably removed soon). Those groups don’t appear in the group list, but can be used in permission settings.
There is a category only for staff, which is the only category not visible to all members of your forum. When your forum requires login for access, categories can still be private in that regard that they are only visible to members, but otherwise, your categories will be public.