The main classification should be done through Options > Archicad Property Manager and Classification Manager. Here you have the default properties, but you can create as many new ones as you need. Each property is than mapped into an Archicad classification schema, which is further connected with the preset .ifc export translators.
The ifc schema can be expanded (File > Interoperability > IFC Translators > Edit / Create Property Mapping > Map IFC Properties For Export), but you should keep the default ifc properties and add instances only. The best way to start tweaking this would be using the default Archicad template, as this mapping is well pre-set there. Try to avoid using the element menu .ifc properties (in your picture), as you'd need to do this every time for each element. Mapping those up front and using Favorites makes life much easier.
Archicad 4.55 - 24 | HP Z800 | Dual Xeon X5667 | 48 GB RAM | Nvidia Quadro P1000 @ Windows 10 Pro x64