Can't copy paste

If this is a sudden problem and has not occurred before then trashing your InDesign preference files, which resets the program to its defaults,  might fix the issue. 

To do so:

For Macintosh Users: The User Library folder in which InDesign’s preferences are stored is hidden by default on most Macintoshes. To access it make sure that InDesign is closed and click on the desktop to launch a Finder Window (Command-N). With this window in column view follow the path User>Home folder (it’s the folder with an icon that looks like a house—it may have the user’s name rather than “Home”) and click on the Home folder. With the Option Key pressed choose Library from the Finder Go Menu. “Library” will now appear within the Home folder. Within the Library folder find the folder called Preferences and within it find the folder called “Adobe InDesign” and the file called “com.adobe.InDesign.plist” and delete both that folder and that file. When InDesign is next launched it will create new preference files and the program will be restored to its defaults.

For Windows Users: You can try the quick way of resetting on a PC which is to hold down Ctrl + Alt + Shift when launching InDesign and respond affirmatively when asked if you want to reset. There have been some recent reports that the window asking if you want to reset is not popping up but that the prefs are being reset anyway. If this works great but if it doesn’t you may have to manually delete them.

To do so: On Windows 7 and above the preference files are hidden. To find them go to the Control Panel and open Folder Options and then click the View tab. Then select “Show hidden files and folders” or “Show hidden files, folders or drive options” in Advanced Settings. Then delete (or rename) the folder at the end of this path: C:\Users\<USER>\AppData\Roaming\Adobe\InDesign\<Version #>\<Language>. Make sure that InDesign is closed when you do this. When you relaunch the program it will create new preference files and the program will be at its default settings.

The advantage of manually deleting preference files is that after you’ve reset up the program (make sure that no document window is open) to your liking, you can create copies of your personalized “mint” preference files (make sure that you quit the program before copying them—that finalizes your customization) and use them in the future to replace any corrupt versions you may need to delete.

Paste pictures? You don't paste, you Place! Pasting is asking for problems...

I have had the same and similar problems (Mac Catalina InDesign 15.0.1). Clear up as much memory as you can and cold restart. See if that helps (it did for me).

Which version of InDesign and OS and how much RAM?