Public transportation to visit Beijing's nearby '清東陵 & 清西陵'

1. Both of them attractions are open to the public!
2. Yes, public transortation is available to the two place.
To Eastern Tombs of the Qing Dynasty(清东陵), many tourism buses can be found at the northeastern exit of Xuanwumen metro station. They can take you there directly!
To the other tombs, I suggest you take a bus at BJ Lizeqiao Bus Station to Yixian first. Then transfer to another direct bus to your destination (there is only 7km between Yixian and the tombs).
3. I remember ther are some farmer resorts or small hostels near/in the two place. You can go to check in on tbe spot!
May help!