Hi whitehotmarketing,
1. To get an this week’s events list you would need to create a custom page with a custom event query on it. We’ve got some examples of custom event queries in our documentation here: https://theeventscalendar.com/support/documentation/the-events-calendar-template-tags-general-functions/#functiontribe_get_events – and, you can also use WP_Query which you can find an example of here: https://gist.github.com/jo-snips/5112025
2. Event category list pages are included by default and you can view them @ http://yourdomain.com/events/category/CATEGORY_NAME/upcoming/
3. Event venue lists are also included by default. If you click on a venue within any event you will be taken to that venue’s page and there will be a list of upcoming events for the venue.
4. There is no current built in feature to allow for searching by date, venue or category. You would need to build something like this yourself if you wanted it now. Good news is though we have this coming soon in our 3.0 release! You can check out a preview of what’s to come here: https://theeventscalendar.com/events-3-0-preview/
I hope that helps but let me know if you have any questions.
– Jonah