Seven barrel Nock type of gun percussion
 

This seven barrel gun looks similar to the famous Nock gun. However, there is no brand on the barrel and lock, and the lock is percussion. Is this a latter imitation of the famous gun from another company?

My guess would be that this is indeed a later imitation. I've seen a couple of mentions of "multi barrel goose guns" which I am going to guess that this is. The fact that this is a "taken down shotgun" format makes me believe it probably would have gone in a nice sporting case at some point.

There is an article on these guns in "The Field" magazine titled "A seven-barrel ‘goose’ rifle", which I unfortunately can't access without a subscription but it shows what looks an example of a gun that looks quite similar in style to the one you showed.

That seven-barrel volley gun is indeed very similar to the Ordnance gun supplied by Nock and appears to have been converted from flint action to the percussion principle via the nipple & drum method. The calibre appears to be the same also, .57 or Pistol Bore. It was most likely for use on a commercial ship.

Goose guns are absolutely a 'thing' and those I have handled have been of smaller calibre. Often the seven bores were drilled out from a single large barrel, rather than a cluster of seven individual barrels, and they will be found with various types of ignition and barrel configuration etc.

Can someone please explain to me how the jet of fire gets from the piston to the charges in the barrels? This is completely unclear to me

The whole construction seems strange and warrants further comment. The means of communicating fire to the outer barrels seems reasonably clear. The centre barrel connects with the percusion ignition and six holes in the hollow breech plug communicate with the touch holes in the outer barrels. Each of the outer barrels appears to have its own breech plug which can be removed with an internal squared key. This explains the strike marks on the face of the barrel group which indicate which plug belongs to which barrel and ensures they are correctly aligned.

What isn't clear is why the barrel group was designed to be removable as this doesn't contribute anything to its functionality. A strike mark on the breech shows how the barrel group is supposed to align but wear on the thread means the barrels no longer align correctly. This suggests to me that it was designed with spare interchangeable barrels mitigating the issue with multiple barrelled weapons which is the time taken to re load. If this was the case then it looks like a somewhat optimistic design maybe in anticipation of a lucrative naval contract.