Hey Paul,
Thanks for your interest in our plugins! This is unfortunately the only feature that The Events Calendar can do all on its own:
Have a general calendar showing all the events in the next month.
For all of your other features, I unfortunately do not have specific plugin recommendations for you, but you could indeed either write custom code to build out these features or hire someone to build them for you.
When it comes to features like these ones:
Enable us to sell the exhibitor space for each event?
Charge our members annual fees?
You can use an eCommerce plugin like WooCommerce to do this. Check out WooCommerce here → http://www.woothemes.com/woocommerce/
WooCommerce has many extensions to it, as well, so if you browse the extensions you might find some exhibition-specific tools there or other extensions that would suit your project well.
Cheers!
George