Is it possible to open second file into Nano text editor not by browsing files in program interface (it's not so usable because you can't do nothing like search etc in it) but in command line or in mc (Midnight Commander) without closing first file? If you can't normally open files it seriously limit possibilities.
No, it's not possible. That's what advanced editors (Emacs, Vim, kate gedit, you name it) are for.
However, it is possible to do something useful, even though more restricted: you can add files to the one you are working on, and you can do so in a moderately effective way. When you say Read (or Write!) file, you may give the command ^T which will open a graphical window, and you can search for the file by moving within this graphical windows as if you were inside Nautilus or Dolphin, or whatever. Alternatively, again after invoking the Read or Write commands, you may issue commands to the shell by means of ^X.