Yes you can't get the HM until you get to vermilion city however if you trade with a friend and that friend gives you a Pokemon that knows flash then you can have flash by the time you reach cerulean city.
Go past mt moon go east and you will be in cerulean city.
The Cerulean Cave is in Cerulean City. You have to surf from a place around Cerulean Cape down to the Cerulean Cave. The Cerulean Cape is north of Cerulean City across the bridge.Go to the north end of the nugget bridge then left down the grass and follow the mountain to it. Btw you'll need flash and you can find Mewtwo in it.
Gym 2 is Cerulean City, and the Gym Leader is Misty ("The Waterflowers of Cerulean City" is the Pokemon episode with Misty and her three sisters). To get to Cerulean City, you need to go through Mount Moon.
Misty is at the Cerulean Cape. It's close to Cerulean City.
None.
Rock Tunnel. Which is located directly right of Cerulean. You must have a Pokemon that knows 'Flash' however
it is in Cerulean cave in cerulean city since u have to use flash u have to look VERY good
It is east of cerulean city, HM1 CUT is needed and HM5 Flash.
Go east(or right) of cerulean city(you'll need flash to get through the cave)
Now you can go through rock tunnel which is east of cerulean city.
Cerulean Cave, outside Cerulean City
Cerulean cave located near cerulean city.
Go past mt moon go east and you will be in cerulean city.
cerulean city
at cerulean city.
Vermilion city.
inside cerulean cave near cerulean city.