Extend Wordpress plugin "The events calendar"

I'm a newb in wordpress plugins, and I need to extend popular plugin "The events calendar" by using hooks in function.php or creating new plugin.

First question, which function.php in which theme I need to use?

In overall, I need to add functionality to sign up for event:

In admin - input field with max participants, subscription checkbox and new tab with complete list of participants;

In frontend - add Participate option: name, email, etc and check if user is in subscription database.

Second, could someone show some starting points how it's done?

Thanks!

via Chebli Mohamed