The airport bus to Zhengzhou downtown will run about 40 minutes and the ticket fare is 15RMB. Ot you can take a taxi, which will not cost you too much, and it is faster. As to the museu, you mean Zhengzhou Museum or the Geological Museum? The latter one has dinosaur fossil. You can take taxi or city bus. Longmen Grottoes is in Luoyang. You can take a bus at Zhengzhou bus station to Luoyang and find Luoyang Bus 81 to the scenic spot.
Can not help the dual-sim cards phone. I just know domestic brands in China has such telephone. They are not expensive and easily to get in electronic product shopping centers.