I have the same panel at the bottom of every screen, on every desktop in the pager,
in every activity.
Is it possible to limit which activities will display the panel?
It doesn't seem to be, if you are talking about the standard KDE panel. But ...
Same question from the opposite side: Can I add a new panel in a particular activity,
but NOT see it in other activities?
There are other panels and docks you could use instead. Some of them behave differently, some don't. For instance cairo-dock
behaves like the standard panel in this respect, but if you add the daisy
widget to the desktop, it will only be visible on the desktop you've added it to. By default it's a circular program launcher, but you can easily set it to look like a panel. (If you want it on all desktops in a certain activity you may have to add several instances of it.)
And even with a standard panel you can, of course, set the task manager to only show application icons from the current activity.