From Shekou to Hong Kong airport you can take the ferry, costs about 250 HK$ I think, and you can check-in your luggage and enter the airport directly in transit, so that you don't need to cross border again at the airport. Or you can go to Huanggang, there is a service of "Limousines" costs 150 HK$ or 120 RMB, a small van will take you to the airport with 4 or 5 other people, takes about 45-50 minutes.
To go to the centre of Hong Kong, you can also take the Ferry in Shekou, or you can go to Lou Hu or Futian Ko Han, then take train to Hong Kong cost should be 100-150 RMB for return ticket. Those places are very easy to get too with the metro (just Shekou and Lou Hu are quite far away from each other).
I know there's also a new bridge but never used it.
Nan Hai hotel, that's a very nice hotel, you can ask for your English tour there they will certainly be able to help you