Sportster carburetor what is the pin and ballbearing that dropped out of the float bowl?

If your motorcycle's fuel system is not functioning properly, it can prevent the engine from starting or cause it to run poorly. One issue that can cause these problems is a faulty float in the carburetor.
The float in a carburetor is a small device that helps regulate the fuel level in the carburetor bowl. It is attached to a needle valve that controls the flow of fuel into the bowl, and floats on top of the fuel in the bowl. When the fuel level in the bowl rises, the float rises with it and closes the needle valve, which stops the flow of fuel into the bowl. When the fuel level in the bowl drops, the float lowers and opens the needle valve, which allows more fuel to flow into the bowl.
If the float in your carburetor is not functioning properly, it can cause the fuel level in the bowl to become too high or too low. If the fuel level is too high, it can cause the engine to flood or stall. If the fuel level is too low, it can cause the engine to run lean, which can cause it to run poorly or not start at all.
If you suspect that the float in your carburetor is not functioning properly, you may need to remove the carburetor and inspect or replace the float. It is always best to consult a service manual or a professional mechanic for specific instructions on how to do this.

Sounds like the float in the carburetor is stuck. Its inside the bottom of the carburetor inside the bowl. The bowl is just the bottom cover of the carburetor..its an empty bowl shaped bottom that fills with fuel...controlled by position of float that works essentially like a fishing bobber. Remove bowl and press the float up and down it should move freely. If there is any resistance or float does not drop down with bowl removed. The pin that holds the float in place needs to be removed and cleaned. I would also wire brush out the bowl and spray it, the float and float pin with carburetor cleaner. You do not need to disassemble the rest of the carburetor to check and clean the float. In the picture the float is #2, float pin #12, I think there are four bolts #14 that hold the bowl on.

You might have a sticking needle valve

The only external adjustment is the low speed needle which is on the side of the carburetor and should be 1 to 1 1/2 turns out. Remove the air cleaner and housing to verify the choke is opening completely.
If neither of those solve the problem remove the carburetor bowl and check for dirt in the bowl. There may be dirt holding the float valve open allowing to much fuel into the carburetor. Also check the float by removing the float pin, remove the float and float valve, shake the float to see if there is fuel in the float, if there is the float will have to be replaced. Also check the float adjustment, if this is off it will allow to much fuel, Place the carburetor on it's side with the float pin up and measure the float height, it should be 5/16 to 3/8 from the carburetor body to the bottom of the float.

Chances are the float needle is stuck closed. Remove the float bowl and spray carb cleaner at the float pin while gently lifting the float then releasing the float to drop freely. Do this several times until the gas starts to flow when the float drops downward. Check also that the gas is turned on and gas is in the tank.

Your Float bowl is stuck. Sometimes it gets a bi of dirt in it and keeps it from seating to turn off the fuel. You need to remove the bottom of the float bowl. This is easiest done by removeing the carb from the bike because you have 4 screws to undo on the float bowl. Really is pretty easy to do.

Carburetors have a Float Bowl on the bottom. This float bowl has a small amount of fuel, that the carburetor uses. (The float bowl's amount of fuel, is replenished from the gas tank. The fuel is gravity fed from the gas tank, through the Fuel Line)

The float bowl has a Float Needle inside. The float needle is attached to the Float. The Float resembles a thick doughnut. On one end of this doughnut, is a flat piece of metal shaped like a U on the end. Looking at this -> U shape, there are two holes at the top. There is a metal pin that goes through these holes, and the pin is attached on it's end's, by the main body of the carburetor.

The flat metal U shape, and the metal pin, works together to form a type of hinge, allowing the float to pivot on it.
Where the U shaped hinge is attached, the float needle, clips to it.

The float needle has a tapered neoprene tip, and sits in a Float Needle Seat. This seat is a barrel shaped piece of brass, and has a tapered hole at the bottom. Fuel comes up through this seat, and the float needle regulates how much fuel can come in.

As the float drops down, it draws the float needle out of the float needle seat, and fuel comes in. As the float bowl fills with fuel, the float rises, and pushes the float back up, also pushing the float needle back into the float needle seat, cutting off the flow of fuel.

There is a specified height of the float, in relation to where the float sits in the float bowl. If the float sits too high, the float bowl fills up with fuel, and overflows. This overflow goes through an Overflow Tube, on the carburetor.
(If the float sits too low, the engine starves for gas)

A LOT of times, crud builds up in the gas tank, makes it's way through the fuel line, and gets into the float bowl. It can get in-between the float needle, and the float seat, thereby flooding the carburetor out, and fuel comes out of the overflow tube.

The float bowl is also attached to the carburetor with a brass main jet nut. At the bottom of the float bowl, this will look like a brass head of a bolt. Under the brass head is a small O-ring. This can leak. First step is too insure this is tight. (Do Not Over tighten! This is part of the main jet, and is expensive! It's Brass)

Where the outer part of the float bowl itself, attaches to the carburetor, there is another O-ring.
A large one. This O-ring, like the main jet O-ring, can deteriorate over time. Additives that gasoline has in it, heat from the engine, and heat from the sun does this. Plus just age. Neoprene breaks down after time.

It could also be that the neoprene tip of the float needle has broken down.

You indicated you adjusted screws on the bottom.
These are the Main Jet, and Idle Jet -> Air Mixture screws. All they adjust is how much air goes through these jets.
The amount of fuel going through, is predetermined by specific passageways, that are drilled through the main body of the carburetor.

This only comes into play when the engine is running. With the engine off, and fuel leaking out, you have crud under the float needle, or one or more of those O-rings has deteriorated.