what web template tags are there?

I found UNITY_PLUGIN_PATH, UNITY_WEB_PATH, UNITY_WIDTH, UNITY_HEIGHT, UNITY_BETA_WARNING and UNITY_MANUAL_DOWNLOAD_URL in the template. Is there a complete list somewhere or is that it?

I'd like to get more of the information from the player settings, like company name and product name.

There is UNITY_WEB_NAME which should give you the product name. Other then that, your list appears complete.