Facebook – the maximum supported image size for a Facebook page

You should use the new Groups functionality to achieve this. Create a group under the same name as your page and think of it as an inner circle to your more dedicated fans. You will then be able to invite group members to the event.

Pages are meant to provide information without being a nuisance to the follower. It is basically an extension of a business or celebrity. The 'fans' term was dropped and replaced with the 'like' term. Users 'like' your page they are not friends/members of your page. It can be a passing penchant. I can decide to like your page today and not like it tomorrow. Hence the way I see it , Facebook Pages can never contact me outside of Facebook i.e. by mail . Potential spam (click-jacking,liking useless pages) headache avoided.

If you really want to use your page you will need to focus on getting more attention to your events by hooking up some fbml and a tab as the default page instead of the wall. Also look into your insights and decide when is the best time/day to update your followers.

You can "like" a Facebook page as a page you administer. For this you need to log-in your account - Then go to the page you'd like to "like" as a page - scroll down until you see the option to “Add to My Page’s Favorites” at the very bottom on the left hand side.

Now click this option and you’ll see a pop-up window, where you can choose from the pages you admin.

That's it.