Dunno on your first question about which version, but at this point I would guess it is the first release of 2.2, not the update for the release.
You do not have to be rooted, "installing" in this sense is just moving the file to the root (base directory) of the SD card. Astro does not root you and the steps you did here, if this is just the 2.2 update with nothing extra, did not root you.
One easy way to check to see if you are root is to look through your app drawer, or full applications list, for a ninja type icon that say Superuser Permissions. If you have this, you are root. If you do not have this, you are not rooted.