No problem – I’ll clarify what I can and we’ll call in @erlend_sh to corroborate (or corrrect).
User Visits: Registered, logged in users visiting your site
New Users: New registrations
Topics: No of new threads
Posts: No of responses to threads (including initial post)
Time to first respond: How long before someone responds to a new topic
I believe the answer is yes, it includes the OP
A session in GA would include unlogged in users as well.
Yes – install the Data Explorer plugin and you can use SQL to query your entire database. I can provide you with a query that will return the number of active members (i.e. have made at least one post) in a given timeframe. You can get total users from the top right of your /users page. e.g. https://experts.feverbee.com/users
Discourse analytics are actually pretty great compared with other native platform metrics. It takes me about 20 mins per month to pull the following (with the exception of DAU/MAU) from Discourse and GA alone.
That said, if you want more insights, both Community Analytics and Discourse Metrics offer useful paid services /cc @Bas_van_Leeuwen and @DiscourseMetrics
Does that go some way to helping you clarify things?