What is the template tag to call the date the article was posted?
This would be pub_date, but it returns a timestamp so you would need to use a snippet to format it (or use some built in date formating available in snippets like Ditto if you are using this to display the articles.
Here is a list of all the available document variables:
http://www.modxcms.com/document-tvs.html
The other questions are less straight forward. For the categories question this could be done either with "tags" or by physically putting the documents in a container (modx folders) and then getting the folder name with a snippet like GetField.
For comments MODx depends on the Jot snippet, I think that it has built in comment counter features.
One thing that you will see when using MODx is that there is rarely only one way of doing things. That is the beauty of MODx, no strict rules.
I recommend that all new comers install a local version of MODx on their PC and study the sample content which includes a full featured blog.