WC Dodge Enthusiasts - Please Help

[rampant rivet]

Looks like a carter carb to me, as to problems I would rebuild carb making sure to replace accelerator pump as this causes flat spot, though it may be that carb body is worn this happens a lot with Zenith carbs, maybe carter too.
Air cleaner should be ok but make sure its cleaned and full to the level with clean oil.
Check fuel lines especially rubber ones as they can perish and allow air into system.
Service engine, new plugs, leads, points Etc check timing and compression.
All these operations should be carried out as routine to enable you to eliminate suspects one by one and to give reliable operation.
hope this has been of some help.

RR.