The third gym leader is Fantina, and she is in Hearthome city. The only way to get there is from oreburgh going through mt. coronet. Hope it helped.
Cobble badge
By beating the first gym, in Oreburgh City.
In Diamond, Pearl and Platinum 7th gym is in Snowpoint Town.
The fifth one in Hearthome City.
You beat the first gym leader, Roark in Oreburgh City.
I have Pokemon platinum the 3rd gym leader always their your probaly just not lucky.
Cobble badge
the seventh gym badge snowpoint gym
you beat the gym leader
Hearthome
Sunnyshore City Gym: Electric (beacon badge from Volkner)
it is Mauville gym
you beat everyone in the gym
beat the league
snowpoint city
beat the #?*@! gym leader
In Diamond, Badge 5 can be gotten by defeating Fantina in her Gym in Hearthome City.