Frame Question

That tube is a frame brace and was a modification on race bikes. It was a fairly common but misguided attempt to improve the stiffness of the frame. No two frames have it in exactly the same place and is often in a different tube size. Whatever, it does nothing useful and should not be there. But it mostly does no harm either so you can ignore it.

Joe Sieffert's Thruxton Racer has that tube (see pics at bottom of page) and he can probably tell you more about it.

https://andover-norton.co.uk/en/our-bikes/detail/555

But that ignition key/ignition switch looks very vulnerable. The original switches had a very stiff plastic cover, damn nuisance when trying to service the switch/connectors. In this case, ease of working on it but???As it is missing, the rear of the switch is exposed to the weather, and tampering.

This bike has been tarted up to sell. No sidestand ties in with the frame mod (as used for racing)
The barrels have had a paint job done on them and they have painted over the base nuts, Rocker covers held on with cap screws, another racers mod. Float bowls on the carbs have no drain caps meaning they are as old (or older than) the bike (and probably worn out). The K & N air filter looks as if it has had a clout. The front engine mounting through bolt has a plain nut fitted, it should be a Nylock one, like the ones on the rear isolastic through stud. Sorry to be a bit of a kill joy but take someone who knows these bikes with you to see it and give it a once over. Ask questions about the isolastic mountings, when they were last serviced/adjusted or upgraded with the vernier adjusting variety.  What kind of head steady is fitted (the early ones broke) Grab hold of the rear wheel and firmly push it left to right To check the swing arm bearings (another problem area)
Look at the swing arm to see if it has contacted the footrest/silencer mounting bolts (another give away that the isolastics/swing arm bearings are knackered) 
Also where is the chain guard? has the mounting bracket on the swing arm been removed? All this i gleaned from the photo, what else lurks there? 

True true, it has an air filter. The deformed K & N is a pointer to something possibly resting against the filter itself and with the engine assembly shaking as much as it does could well mean the filter getting holed at some stage, something else to check.
Yes i never liked the keyswitch down the side.... 

It's hard to tell from the pic exactly what is going on, but as far as I can see the rear brake pedal is connected to a cable inner which is anchored on the stop for the cable outer.

At the right price it is a good basis to improve upon. It is 53 years old..
j

That looks like a nice bike and as with any Commando you can improve and personalise to your own taste as all standard and custom parts are mostly still available.
In my opinion a well set up commando is the best bike in the World which sounds great, handles well with great performance and excitement.

Despite all the above, where is the engine number. This bike has a very suspect history. Why go the expense of a nice paint job and not fit a chainguard. Sadly this bike I would not touch unless it is cheap, very cheap.