I am trying to create a 'qtoolbar' within a 'Qtabwidget'. The Qtabwidget is within the main window.
1 - Ah, this is a Microsoft "ribbon bar." It's really a menu where the menu items are represented as groups of icons that appear below it. There is a commercial product called "QtitanRibbon" that does this. I don't know if that is an option for your project. There is also a QRibbon project on SourceForge which has been inactive since 2014.

If you want to implement something like this yourself, I think I would start by using QDockWidget as a container for a QTabWidget. The widget contained on each tab would contain the buttons and groups for the commands for that tab. This is not an easy project.

3 - Wow, you set high bars for yourself. Basically, you would use QTableWidget::setCellWidget() to set a QComboBox in the cell. I have no idea how you would insert a combo box into the popup as your example shows. I think ultimately you will need to design a custom combobox widget for this and use it as the cell widget.

4 - This isn't available in QTableView / QTableWidget. You might be able to use QTreeView / QTreeWidget for this, but tree views don't draw grid lines. Maybe something like CuteReport can do this.

If you are developing this GUI as part of a project and not for homework, there are a lot of resources out there, both commercial and open-source. Using / adapting some of these might save you a lot of work. Look at the inqlude site or under the "Qt Programs" topic on linux-apps.com.