I will be removing Ubuntu from my system but I would like to keep Unity shell in my system. As the other distro I use is a Arch distro so Unity can't be installed there. So can I install a bare bones Unity 7 shell in my elementary OS 0.4 ????
Installing another desktop environment on elementary OS will probably break things. The elementary apps are designed for GTK+ and Granite, and they may not work properly under Unity. Additionally, I don't believe that Pantheon Greeter provides a way to choose your desktop environment at login. [Edit] I may be wrong about that last part - see the comment below!
See also: this comment on installing the Budgie DE.
If you'd still like to proceed, I'd recommend setting up elementary on a virtual machine and trying to set up Unity there before trying this on your primary OS.
Do you mean the terminal emulator? if so ubuntu use's gnome-terminal? or do you mean install a just ubuntu system with no xserver? "Unity" is the desktop flavor along with the display manager that it comes with im not sure what a unity shell is.