Also as @mtmail mentions, the better path for this is probably not on the device itself. It would get expensive where N number of users is really high. Perhaps at the service layer, send the device location to the service, and have the service return the nearby users.
Assuming you have the coordinates for the each online user, iterate that collection, create a CLLocation object from the coordinate data, and check that object against CLLocation method distanceFromLocation with a radius value.
I have worked with Ext JS for quite some time. Started with Ext JS 3.x and more recently Ext JS 5. Mostly large financial applications. Full disclosure that I am a proponent of Backbone, and Angular too. Right fit for the project.
Ext JS 3.x did what we needed it to do and did them well; grids. Lots of grids. Other than that it was kind of difficult to build a single page application without routing since Ext JS 3.x didn't have anything built-in, so we had to make our own. We used Ext JS 3.x less like a framework and more like a utility. There were some pain points around the REST aspects as well. Remote data with Ext JS can be difficult.
We found that after moving to Ext JS 4.x everything was more polished. The ability to theme with SASS, mixins, etc. The MVC pattern was a big plus. Performance was faster, and the integrated builds Sencha introduced with Sencha Command were excellent for automation. We still ran into problems with internationalization, which Ext JS 4.x does support in its own controls, but you have to roll your own for content. There were also some pain points again with remote data. Still much better than previous versions. Ext JS 5.x is building on the MVVM pattern and adding a number of great features. Migrating and upgrading to new versions is actually much more streamlined and automated.
One topic I want to point out that throughout any of the projects I worked on with Ext JS the remote data was always the pain point. Every single, time. On a large scale project usually teams are split up, UI, middleware, etc. We found that you had to design the REST endpoints carefully with the middleware team so that they worked well with what the Ext JS proxy expected. Like pagination for a simple example. You can customize and extend Ext JS of course, it is just we found bending Ext JS to meet another teams interpretation of how a REST endpoint worked was really difficult. Granted that comes down to communication, but even then I still saw problems. There are plenty of others on the Sencha forums.
I like Ext JS, I think Sencha has a mature product. Excellent support and a great community. Like any framework, it has pros and cons. I can't speak to Sencha Touch as I do native iOS, but I am sure it is similar as they share a lot of the same concepts.
Other frameworks like Angular, and Backbone I usually lean towards though as they are the groundwork, a foundation. They allow me or a team to build an application without getting in the way too much or dictating how.
I do not see why not if you are motivated enough. I would even pursue 'social coding' on Github. Seek a project out and see if you can contribute? Learn from others after you have the basics down so you can ask constructive questions and hone some skills. Could serve as a mentor of sorts that you are seeking.