Chris,
The indicator is a passive piece in that it is not under spring tension nor is it accuated by any type of mechanism. It is mounted in the cocking lever through the hole in the sear arm of the cocking lever that can be seen in your photos. Its motion is delimited by the cut on the right side of the breach block. The indicator consists of an ear and an axle. The axle is longer than the depth of the hole in the sear arm. The axle is a tempered spring that has been split along its axis that has two ears on the far side that expand outward when the indicator is fully seated in the hole holding it firmly in position.
The cocking lever is retained with the action lever pin and these two parts move in unison when the lever is lowered. When the sear arm of the cocking lever snaps over the trigger engaging the sear the striker is in its full rearward tensioned position and the action is cocked when the breach block is raised. Additionally, the striker arm of the cocking lever holds the striker rearward until the sear is released.
As the sear arm rises it rotates the cocking indicator through an arc upward enough that its tip becomes visible above the breach block. When the striker is released the sear arm of the cocking lever rotates down lowering the tip of the indicator below the top of the breach block. Just as a note, it is unsafe for the striker to be down when the action is closed and there is a live round in the chamber as the striker does not rebound or retract from its full forward position. At a minimum when a live round is in the chamber the action should be open. The forward part of the breach block will block the round from falling out of the chamber as the striker spring holds this position only allowing the cartridge to be removed when the lever is pushed under striker spring tension fully forward thus lower the breach block fully.
Some observations about your rifle. It is very nice rifle. Notice the difference in serial numbers between yours and the one that I photographed. Yours has the cone at the back of the action assembly like the BSA and Cadets rather than the cross pin through the action. Second, yours uses an eared extractor rather than the hemi version of the rimfire BSAs and of the my Francotte. Interestingly, Hoffman and Griffin and Howe custom rifles have modified rimfire extractors just as I did my multi-barrel project by simply putting the rim cut in the hemi version. From what I've seen of the early American gunmakers' use of the Martini actions they are pretty much Model 12 BSA rimfire.
The cocking indicator of the rifle that I have been photographing is quite wide compared to my BSAs and I'm not sure which might be appropriate for your rifle. I think one could be easily made and if you have a photo of the rifle from the auction house you may be able to discern which style it has. In my visits to Gunparts I have never seen a cocking indicator available.
Your trigger has been tuned by beveling its rear engagement surface to reduce apparent weight as well as to create a crisp letoff.
Finally, the takedown system is a surprise. I expected to see threads and then a cross pin that had a cutaway when 'opened' allowing the barrel to be screwed out and with a cam that actuated into a channel that went through the threads when the pin lever was rotated 'closed'. How tightly does the barrel tenon fit with the action?
I think that your sticky in and stickier out issues with your firings warrant close examination before more shooting and after you are sure what the chambering is headspace checking is in order. The firing pin appears to be a larger diameter than the 1/16" that I have been using. I can't tell whether the pin is bushed but it is also advisable to ensure that the pin has a good snug fit in the hole.
I'll let Mike address chamber casting.
Sorry for the lack of brevity but hope this helps.