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What does it set the og:type field to?

By default this is blank. Can be set using the admin screen under the Settings menu. I would probably set it to 'product'.

How do install a facebook like button, without using another plugin?

Since 1.4, this plugin can now print the 'Like' button code at the bottom of the product page for you. Just enable it in the settings page and you are done! You can also change the code used to print the like button. There is an example in the default code to use the 'Comments' plugin instead of the 'Like' plugin.

I want to add my own Like button code to my template. Can I do this?

Sure! Just disable the automatic printing in the admin screen, and add your own like button code to product.php or wherever you want to put it.

Why do you print fb:app_id and fb:admins on every page, not just the product pages?

This allows Facebook Insights to check your page. It needs these tags in the homepage in order to validate your domain. With this enabled, you can see all the likes you have received for every product in your whole shop. You even get a pretty graph!