What if I am not staying in a hotel for completion of visa?

I currently live in China. In September I am moving to Moscow. I will be stopping to pick up a bag. I will fly to Beijing from my holiday in Ireland and then to Beijing. I will be going to Yantai getting my suitcase and going back to Beijing and flying to Moscow.

I am not sure if I need to fly to yantai, if that is allowed, or if I will take the train, if that is allowed?

I need to know if I don't stay at the hotel, as I have plenty of friends. If I am eligible for the 72 hour free transit. And am I allowed to leave Beijing?