Cannot drag program to second monitor when program is activated

Switch the second screen to a different desktop, then drag.

For example, in Mission Control, the top of your second screen might look like the picture below (Finder is fullscreen, and there is another "Desktop 2"); you could switch to "Desktop 2", close Mission Control and then you would be able to drag a window from the other screen to this one.

You can't have an application in fullscreen and another one on the same screen.

(You can, however, use split view: put two applications side by side sharing one screen.)

Using Mission Control you can have multiple virtual desktops on each of your screens. I believe F3 is the key to enter Mission Control. Click + at the top to add another desktop. Applications in full screen automatically get their own individual desktop.

One can switch between desktops with control-left arrow and control-right arrow.

Not exactly sure how that works with multiple screens but if you click a menu bar on one screen it will make that the “active” screen so the desktop should change on that (I am not at my mac and would not have a second screen to test until probably tomorrow at work anyway).

Do you have Finder in full screen mode on the second display? You can either exit full screen or you can use another “desktop” on that screen.