Have the ability to sort the calendar view by category type, search by category, being able to subscribe to a category to be notified when an event is posted in that category. All while being able to see all the events in all the categories in one place too.
Um, because the default minimum for MySQL full-text search was set to four characters for years. When Version 5.6.4 was released (I believe) it was changed to 3 characters. They are still supporting MySQL 4 (suggesting MySQL 5 though) for the 3.x series hence the four character limit out of the box.
Are you wanting your calendar entries to post to twitter or take a twitter feed and post it to the calendar?
If you are wanting your calendar to post to twitter. Set up your calendar to have an RSS feed and then use a service like http://twitterfeed.com/ to take your calendar RSS feed and post to your twitter account.
There is currently no way out of the box to take a twitter feed and post it to the calendar.