WP has a note on the stats page, saying, "...we don't count your own visits to your blog." But WP DOES count my visits when I'm NOT logged in
That is correct. It is only when you are logged in that wordpress.com knows that it's you.
If a visitor lands on my site, is that a "view?" If so, how would it be distinguised from a post "view?" How is a post "view" determined?
A view is a view on your home page, your page pages, your category pages or tag pages or archive pages or search result pages. Page views (a real page that is) and post views are separated in the stats, views of the home or category or tag or archive pages are not, but they are counted in the total.
Clicks page of my stats seems to count clicks on links going to other areas of my site, as well as links going outside my site. Is that correct?
A click is a outgoing click or an internal click that brings up a media file (e.g. an image). Click on links to other posts/pages do not count.