Well, ne doesn't have a "block" option. Likewise, it doesn't support any mouse operations, so "clickng again" isn't going to affect ne. There seems to be some confusion about copying text.
There are two completely unrelated "copy" notions at work. First, there is the system clipboard which enables passing data between programs and various parts of the user interface. With text in a terminal, you can click-and-drag or click at one end of the text and shift-click at the other, which usually highlights that text and makes it available in other programs, typically pasteable with the middle mouse button. However, ne knows nothing about the system clipboard.
Second, there are "clips" which are internal to ne. In ne, you set a "Mark" -- usually with Ctrl-B. The mark stays put, and all the text between the mark and your cursor is "selected" -- though not highlighted. You can do several things with selected text: you can Erase it, Copy it to a "clip" (which, again, is internal to ne), Cut it which also copies it to a clip but removes it from your current text, or you can pass that text "Through" an shell command or pipeline. One interesting shell command you could pass the text through is
xclip -f
That will have the effect of copying the text between your mark and your cursor in ne to your system clipboard. You can then go to some other program, middle-click your mouse, and have your text show up there.
But this is all just background. It isn't clear to me from your question exactly what you're confused about. I hope the above description clears up something for you.
As for your second question: yes, ne supports a wide range of characters.