Hello all,
The thing to know about the plugin is that it uses custom post types. So basically, each calendar event is technically a WordPress post. Searching for events would work the same way as searching so-called ‘regular’ blog posts. If the postal code is in the post (i.e. the event description), then it should show up in search results.
A WordPress guru named Joost de Valk really doesn’t like the inherent WordPress search function and writes about other solutions. Here is one: http://yoast.com/wordpress-search/
If you want an events map to be searchable, well, that’s a custom coding project and needs to work with the Google API.
Regarding mobile, I’m assuming you’re asking if the Events Calendar is responsive? It’s not bad, though as far as I know there aren’t any immediate plans to make the calendar responsive as an out-of-the-box plugin. However, you can always set this up in your CSS on your own by customizing the calendar. As long as you follow the responsive rules of CSS design, you should be ok. You will of course want to start with a responsive theme. It’s hard to make anything 100% responsive, but I’ve heard that Brandon at Epic Era’s (http://themeforest.net/user/epicera/portfolio) has good themes. While not always 100%, those themes are responsive and the plugin tends to work pretty well straight out of the box with them.
Hope all this helps!