It is better to create a new thread with your questions rather than post to a very long and old thread. That just makes it harder for the next guy.
1) Yes, MySQLi works with the latest version of Dreamweaver. I use it almost every day.
2) If you download and install the version in your order history it will be the latest. Simply reinstall if you think yours may be out of date.
Maybe start a new thread and tell me the error you are getting. Most likely it is an issue with the site definition and the testing server settings in Dreamweaver preventing Dreamweaver from making the connection.