Hi Mark,
If you undo screw A, underneath it is a washer, and underneath that, a groove. Your throttle cable needs to sit in the groove. As you tighten screw A, the washer pinches the throttle cable in the groove, holds the throttle cable outer still, and allows the inner part to slide back and forth. There should be a mark on the cable where it has been attached before and 'squeezed' it. This would be a good place to start with, when re-attaching it. The cable needs to be in just the right place when you tighten screw A, so the movement of the throttle lever is allowed to have full effect on the carb. (This must be right for the engine to run properly)
Between the holes in the two parts marked B, there needs to be a solid wire. The part marked B on the left, is the part in the carb which, as it rotates back and forth, allows more or less air/fuel to the engine, increasing or decreasing engine speed. (This must be right for the engine to run properly)
Your model number indicates you should have a pneumatic govenor. This operates by the fins on the flywheel making a draught blowing against a vane (a flap) inside the flywheel housing (Faster engine speed, more draught) This vane is hinged and attached to a stiff wire. Having your flywheel cover off, will effect the proper functioning of the govenor. Part B on the right should attach (perhaps not directly but through a linkage) to a stiff wire coming from the govenor. That may be what is already attached in the photo.
The screw marked C, would secure a part (which as you say, is missing) which the throttle cable attaches to. This part also attaches to the part B on the right. It should also have a spring attached (or be linked to one) which balances the throttle cable movement. The thick wire that looks like a spoke probably attaches to this also. (This must all be right for the engine to run properly)
The electrical wire is almost certainly your engine stop wire. When it is earthed (touching a part connected to the metal body of the engine) the pulse of electricity produced by the coil goes to earth (and not the spark plug) so the engine stops or does not run). This is attached to a part which would either be: under the screw of part B on the right, or (more likely) on the missing part which should be on screw C. It works by: when you push the throttle all the way to 'Stop', you are pushing the throttle cable inner from left to right in the photo, and it will turn a part which then connects that stop wire to earth. (I'm not familiar with this make of rotavator, so there's a chance that this mechanism (which connects the wire to earth) might be in the actual throttle lever itself, or in a stop/go switch or key switch, and not on the carb). This is not essential for the engine to run properly, but without it you cannot turn off the engine, without shorting the top of the spark plug to earth or pulling the high tension lead off the spark plug (you will only do this once
)
The thing in the background of your photo with a red circle, that looks like the end of the breather tube. Don't think it's attached to the screw, is it?
Briggs and Stratton had lots of different options and without having the machine in front of me it's hard to say more. It would have looked 'something like' the diagram attached. There is a Snapper tiller brochure for sale on ebay, where you can just make out the carb in a photo. (
https://www.ebay.co.uk/itm/153797633386?hash=item23cf0da56a:g:hbAAAOSwBQ1eH2j0 ) Hope that helps.