Hi Linda,
Here is my attempt at your questions, I do have a bit of trouble framing some of them into Discourse concepts, but here is my shot nonetheless.
Yes they are, we do not expose this in the UI, if you click the link glyph under the post, 
you can see a link to a specific post with the post number.
A theme could add numbers if it wished, but we always opt to decrease visual noise on the screen by default.
Check out our advanced search page for most of the options Search results for '' - Discourse Meta
You can both tag and categorize topics, as an administrator you can also tag messages. That allows you to split related topics into buckets.
You can quote stuff ^^^ like this or just reply and we carry a relationship
This is an email kind of concept every user has a user page that covers full user stats, additionally you have Discourse Meta
I think tags is what you are after, but I am not sure.