As far as I know, only calls without "-nw" support mouse actions. I may be wrong because I have seen vim have some mouse support.
Arrow keys? I don't know why they dont work for you, so I support the answer asking that you check your TERM settings and add that a way out is to either try a different build of emacs, or forget your default terminal and fire up xterm & or rxvt & prior to any emacs -nw work.
To answer your question on menus... look here:
http://stackoverflow.com/questions/191312/how-do-i-get-to-the-menu-in-emacs-in-console-mode
You'll get a dynamic pop-up that simulates your having pressed the menu-summoning Alt key and doing a text-mode navigation. For example, quitting emacs is as easy (or hard) as hitting F10 and pressing f and then q. The problem is that the default terminals on Macs, and Ubuntu 10.10 eat up that key press to trigger their own functionality, like the gnome-terminal menu or the MacOS Dashboard.
You have to turn off the feature depending on your OS or terminal's keybindings. Macs have a System Preference pane to do that, and gnome-terminal has preferences in the Edit menu. I don't remember if cygwin misbehaves and what the fix was, but I know it was working for me.
If you meant having a visible menu... it depends on your emacs version, whether you see one by default. On MacOS I don't, but on Ubuntu it shows up by default without any .emacs file configuration. You probably can make it work permanently by editing (or creating) ~/.emacs and adding the line
(menu-bar-mode t)
You can comment that out at any time by using the ;; comment marker.
PS: You'll have the sad realization that this menu bar in your no-window mode is just a decorative gimmick, and does NOT take mouse input. So it's just there to show you indirectly the language mode it's using (by what menu headers change to as you switch from .sh files to .cpp and so forth)