After you defeat Bugsy, head to the left, into the Ilex Forest. If you have not already, you will be stopped by your rival, and challenged to a fight. In my experience, it was relatively easy. Once you defeat him, i recommend going to the PokeCenter and healing up. Go into Ilex Forest, and there will be a man there, he stops you, and says something about his master's Farfetch'd being gone. Do the task and get both of them back. Once you do, you will be granted with HM01 Cut. Which will allow you to continue on.
When you beat the elite four.
beat the Pokemon luegue then go to the Pokemon centre
nothing
after you beat the gym
Where you beat Brock. An old man is standing in a garden.
When you beat the elite four.
With Pokemon.
Pikachu
go to prefacer.oke then you get one stear pokemon
go to the place that you beat lance.after you beated him for the third time,hike up Mt.Silver and beat red to train your Pokemon to lv.100.
You finish Pokemon heart gold after you beat red.
beat the Pokemon luegue then go to the Pokemon centre
Yes
They are still in the Pokemon league
Yes.
nothing
you gp to seafoam islands