HA has 'integrations' which are plugins for all kinds of services. ZHA is their own one for Zigbee. zigbee2mqtt is a third party one for zigbee, and there are plenty of others. There's an app store type interface to install them (actually two interfaces, because Hassio have their own plugins in addition to HA's).
Yes. Each device has a different way to pair which should be described in its instructions.
Theo