Is it possible to achieve similar results to Pivot Tables in QGIS table editor so as to use just QGIS instead of several software solutions? Or are there maybe some plugins capable of achieving those dynamic results?
The dynamic part isn't really doable without actions or triggers (or some other workaround) - that's one of the key differences between a database and a spreadsheet. However, there is a plugin for QGIS that provides pivot table functionality called GroupStats.
As an aside for any Arc user who comes across this, ArcGIS has a Pivot Table tool at the Advanced license level.