Setting up user locations and categories

I want to know whether it’s possible to set things up so that when a user creates a profile, they can a) set their location, b) set a service category, and c) have this information plotted on a common map. As such, it will be possible to search for a user based on their location AND their service provided simultaneously.

For example, if a non-registered user wants to find a hairdresser in a specific neighbourhood, they could do so based on where a hairdresser has listed their location. I’d also like to have a MAP that displays the same information, and can display it for more than one registered-user at a time. For example, I want to search ALL of the hairdressers in a specific neighbourhood, and these show up on a map, with the users profiles linked. I hope this makes sense!

site is http://www.theexchangemarket.com

I can provide credentials if needed!

Thanks in advance! Happy New Year, everyone!