I have an empty activities screen. Can I put an icon/widget there to open Firefox with some command line options like profile name?

You can create custom shortcuts in the Desktop folder via: right-click -> Create New -> Link to Application. There you can include specific cli flags and such.

You can create these shortcuts in any folder location and clicking on theme in Dolphin will launch them, or you should be able to drag them onto the Desktop. Creating them in the Desktop folder itself will create the icon on the desktop automatically. Creating or linking them in ~/.local/share/applications will allow them to show up in the application launcher menus.

I have attached links to two screen shots. One shows the default screen. The other shows what happens when I right click on the screen.

https://drive.google.com/open?id=1RSE2z ... dc8cdeyDrM

https://drive.google.com/open?id=1497wr ... bE_bYvTmXF

As you can see there is no Ceate option. I have seen this when I am in Desktop mode and not in Activities mode. How do I switch to Desktop mode? I have looked through all the the options on any Settings screen I found.

Checking those screenshots, that's definitely Gnome Shell running, not Plasma. Gnome shell has its own concept of "activities", which as I understand it is basically virtual desktops that Gnome Shell manages: instead of having a fixed set of desktops, it automatically creates and removes them as necessary. Plasma's Activities are a different take on desktops: instead of automatically creating or removing them like that, they are individually customizable, allowing you to set up custom layouts as well as allowing certain settings to be configured per-activity (such as power management settings).

To switch to Plasma (assuming you do in fact have Plasma desktop installed), you need to log out, then from the login screen there should be a menu you can use to select which Desktop Session you wish to log in to (should include options for Gnome Shell, Plasma Desktop and any other desktops you may have installed).