First question: It would require editing the template (i.e. wp.php) to suit your needs, and/or adding any css elements to it that you use on the rest of your site. A good place to start for help:
Second question: With WordPress set up in it's own (sub-)directory, you could rename it to index.php (removing the current one in your blog's root).
A more complicated method is to copy wp.php as index.php to its own themes directory (wp-content/themes/), set up a stylesheet (style.css) with it that provides a stylesheet header, and activate that as your blog's theme. Then load the index.php in your blog's root into your iframe.
Either of these will work if you're not expecting to have a theme'd copy of your blog running as well.