On PC if you go through the SU menu you can only have the one instance. If you go to the SU launch icon or an SKP file in windoze explorer (not IE!) you can as described above open a second copy of SU alongside the first.
Whilst it's sometimes quicker just to double click, if the faces you are push-pulling are all painted with the same material, or all on the same layer, you can firstly right click one face and select all faces with same material/layer, then use JPP. It's then only a two step operation and very fast.
Well I guess the problems depend on what you are modelling. But most people find that drawing directly onto layers other than Layer0 (as opposed to drawing on Layer0, grouping then moving to another layer) almost invariably leads to a complete bird's nest of a model...faces on different layers to their edges...groups and components on different layers to their contents.
The mantra for almost every serious user, right from the earliest days has been "Always draw on Layer0"