The modifications can be done in the same way as adding a thumbnail.
We are not able to help on every step of the way, but here is some more information.
You might want to try this function for event categories:
tribe_get_event_categories();
The Events are custom post types so you can use the Content or Excerpt functions in WordPress to get the description and get it to the length you would like.
Not sure where to link the tickets as I do not know the plugin being used to sell tickets.
And the placement of the coding is up to you and how you would like it.