Splashtop supports text copy/paste via the clipboard. Currently, the copy/paste functionality supports up to 256KB of text for the clipboard, as of v188.8.131.52.
Images are not supported for copy/paste across devices. If you want to transfer an image, best to use the file transfer feature. How do I transfer files?
Starting with version 184.108.40.206, there is a paste clipboard function that can be used to "paste" into fields that do not accept copy/paste into them, such as the Windows login screen. This function translates the copied text into keystrokes.