In answer to your questions:
1. Vantage doesn't specifically handle locations outside of selecting the location from the map during the listing process. If you're looking to have a multi city setup you could potentially look at
WordPress multisite with an instance for each location and selection from the homepage (would require customization)
e.g.
location1.yourdomain.com
location2.yourdomain.com
etc
Or set up the categories as locations.
2. Whilst the demo site is fully functional, you cannot save data to it, so you cannot complete the listing process. There should have been a message to clarify this before you entered the demo site. Vantage is responsive though, so is designed to be used on any device.
3. We don't officially support third party plugins, so unfortunately cannot guarantee that these will all work out of the box. You would likely need additional customization in order to make this plugin work correctly.
4. Yes, locations are handled through the Google maps integration.
5. You just need to set your location within the themes geo settings as shown on the
Vantage admin demo.
6. Not currently out of the box, no. You can read more about this
here. We do not have a confirmed time frame for when this may be ready for our other themes aside from ClassiPress.
7. Vantage will search across title, description, categories, tags, address, phone, facebook, twitter, website URL and custom form field values as well. Thanks.