Yep, Carter BBD. That plate you are manipulating with your finger is the choke plate, the throttle butterflies are at the other end of the carburetor.
The plate is pulled open by the vacuum dashpot at the rear of the carburetor. The silver colored thing in the intake manifold with the rod that runs to the choke is the choke thermostat (I call it the choke coil). It is a wound spring (like a clock spring) that expands when heated and should allow the vacuum dashpot to pull the choke open as the engine warms up. It sounds like yours in frozen.
The choke rod should move fairly easily. If it does not, carefully remove the choke coil from the well in the intake manifold and soak it with a penetrating oil. While the choke coil is out of the well, check to make sure the rod is securely attached to the spring. Replace the choke in the well and work the rod up and down. It it doesn't move smoothly, it should probably be replaced.
