First of all, please think about all the questions you have, before you post and put all of them into one post, there is also an edit button, so you don't have to answer yourself.
First of all, if you go to your forum you can analyse the HTML code of your Login box there, and more or less copy the whole thing into your HTML template. (Right click view page source, or use Firebug Extension)
If you want to show users only, you need to take this information from the Database, which needs PHP. HTML can not connect to the database directly!
Register and Help Buttons to the forum, are just plain html links, go to your source of the phpBB and you will find them, just copy them to your template (links look normally something like <a href="#" ... |
