If a graveyard is full with bodies, then the next body is to be buried so the people go back to where the first body was put. Incase they find bones there, are they to be removed?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.

It is not permissible to dig up the grave of a Muslim except for a necessity. The necessity, for instance, is if the place is not enough and there is no other place to bury the dead except by digging the grave. So if this happens, priority should be given to a very ancient grave, the corpse of which has been transformed into earth. However, if one finds bones in ancient graves the corpse of whom are thought to have been transformed, as you mentioned in your question, then the bones of the dead body would be gathered into one side, and the new dead would be buried in another side. Nonetheless, there is no harm, and some scholars consider that it even desirable, to put a partition between the two. 

Allaah knows best.