How long does it take from Huangxian County, Longkou to Rongcheng, Weihai by bus? Is there a through train? How much is the charge?

I looked it up for you. Although there is no through train from Rongcheng to Huangxian (Imperial City) in Longkou, Longkou is bound for Rongcheng Shidao:

Return route: from Rongcheng Shidao, Weihai, via Rongcheng, Weihai, Huang Wu, Laishan and Daxindian, to Longkou Imperial City;

There is also a route: from Shidao via Rongcheng, Wendeng and Mu Ping to Longkou Imperial City (without going through Weihai).

Because Long Fu Bus Station (private) of Longkou Imperial City has shuttle buses to Rongcheng and Shidao every day, the route of the former is "Longkou-Weihai", with two shifts in the morning (6:40/7:40) and one shift in the afternoon; The latter route is "Longkou-Wendeng", and there will be one in the morning (7:00).

The whole journey from Rongcheng to Longkou Imperial City is about 240.5 km /4 hours. You can estimate the time and take a bus back to Longkou (drive around noon) to Longkou Imperial City. I suggest you call Rongcheng bus station first to confirm.