Where should GEOS libary be located...

Good question, and we really should include this information in the documentation: http://docs.farmos.org

I created a task for it in the documentation Github: https://github.com/farmOS/documentation/issues/9

Basically, you need to install GEOS in the server-level - not in farmOS/Drupal. It is a geometry library written in C++, with a PHP extension that allows PHP to access it.

Depending on your operating system, there are different ways to install it. You can find binaries, as well as instructions for building it from source at https://trac.osgeo.org/geos

One thing worth mentioning: the Area Generator module is OPTIONAL - and it might not do what you think it does. You do not need it in order to create areas. You can do that simply by clicking "Add an area" in the areas list page. The area generator is a tool for generating a lot of areas in bulk - specifically for making it easier to break up a field on a map into numerous parallel beds. If you're not working with fields and beds (I don't think you are, right Sam?) then you do not need the Area Generator tool.

What we like in Area Generator, is the parent/child structure for area

Actually, the parent/child structure is independent of the "Area Generator". You can disable the Area Generator module, and areas can still be arranged hierarchically. The Area Generator is really more of just a "Bed Generator" tool right now. So it's just an extra add-on tool to make it easier to generate the polygons of many beds within a parent area. You don't need the area generator to do that, though, it just makes it easier.