I recently completed a life sized Lego version of the M363 Remote Projectile Detonator (aka the sticky detonator or rocket pistol) from Halo 4. To answer your first question: No it does not shoot. 
Main Photo on Flickr: Link
Additional photos on Flickr (with some work in progress shots): Link
Working features include the grenade being removable, a moving trigger, and a foldable screen. Video on YouTube: Link
Thanks for viewing! Next Lego life size weapon I’ll have is the Halo 4 Battle Rifle, which there is work in progress shots of that on my Flickr.
Nick
