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How can I get the short link in my theme?

Use the twitter_link() function in your theme (within the_loop) that returns the shortened URL. For example:

if (function_exists("twitter_link")) { echo '<a href="' . twitter_link() . '">Twitter Friendly Link</a>'; }

Do I get backlinks counted by search engines with this?

Yes you do. TinyURL links give backlinks to TinyURL.com, while short links generated by this plugin give direct backlinks to your website. This is good for SEO.