Hi Joseph,
You can handle both of these issues pretty easily:
Home - you can redirect /index.php with a few simple lines in your site's .htaccess file:
RewriteBase /
RewriteRule ^index.php$ - [L]
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule . /index.php [L]
However, instead of adding these lines manually, you can simply turn on "Pretty Permalinks" in WordPress (see http://codex.wordpress.org/Using_Permalinks for more details), and they should get added automatically.
Blog - since you're using WordPress, I recommend installing Yoast's SEO plugin (it's free - http://yoast.com/wordpress/seo/). Then, you can correct the ?author=1 issue by disabling author archives. Here's a quick reference for other functionality offered by the plugin: http://yoast.com/articles/wordpress-seo/
I hope that helps!
Cheers,
Steve