Celadon.. I think, wikiepdia.org
Get the bike voucher then go to the bike shop to receive a bicycle.
There are no running shoes in the Red Version. You either walk or ride a bicycle.
see How get bicycle in Pokemon leaf green?
In the bicycle shop in Goldenrod city
Red Zinger Bicycle Classic was created in 1975.
Red Zinger Bicycle Classic ended in 1978.
Yes
Bicycle Shop in Cerulean City ( EXPENSIVE )
You have to talk to the CHAIRMAN of the POKEMON FAN CLUB in VERMILION CITY, he'll give you a BIKE VOUCHER for listening to him, take that to the bike shop in CERULEAN CITY for a new bike.
Goldenrod City
You get it as you enter Nimbasa city.
Yes