No, the flow isn't increased when you hold your finger over the hose. That is, you're not supplying any MORE water....the faucet was never touched, so there's the same amount of water being supplied to the end of the hose. You're just trying to squeeze the same amount of water through a smaller opening. However....yes, the flow will be decreased if you pinch the line, but that's not going to solve your problem. The problem will still exist, it just make take a few more seconds for it to manifest itself.
As to your other question....the hinge pin (actually named 'float shaft') is the small rod that the float hinges on. That rod slides down into two grooves, one on each side of the fuel bowl. Then there's a clip that connects the float shaft to the fuel inlet seat.
If this clip was missing or not properly attached, as the float rises in the fuel bowl, it's going to lift the needle valve off the seat too, holding it open....thus, not shutting off the flow of fuel.
Here's a large-scale schematic of the 2-barrel carb. You can see this clip (called the shaft retainer) as Basic Part No. 9599.
CLICK TO ENLARGE