Once you beat the second gym leader (the water lady), north of the gym is a house and an officer standing next to it. Beat all the trainers on the bridge near that, and keep heading east. There is a house and a boy in there who is shaped like a Pokemon. Talk to him and help him by pressing on the computer in his house. After that, he will come out; talk to him again, and he will give you the S.S. Anne ticket. Go back to the house with the officer, go inside, go outside (toward north of the house), and you will see a rocket gun there. Beat him in a battle, and he will give you dig.
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dig
I think you need a Pokemon with a specialy natural ability that will dig up items if you walk over them.
Go to cerulean city see the house with the guard in front of it later the guard will move and you can enter the house go through the hole in the wall fight the team rocket member he will drop dig
Yes you can trade leafgreen version Pokemon to another leafgreen version.
Use the itemfinder at the spot where mr fuji once stood at the top of Pokemon tower you should dig up a soothe bell. where mr fuji was standing use your itemfinder there