How many Endogenous Retroviruses do we share with other primates? Is there a list of Endogenous Retroviruses that we share with other primates? I would like to map all (or most) of them into a hierarchy and see how it fits in our evolutionary branch.

There are several papers that cover this. Briefly, humans share the vast majority of their ERVs with other primates, but not all; and this is mainly because other primates have acquired ERVs that humans have not (rather than humans acquiring new ERVs themselves). The third link, in particular, seems to cover your proposed reconstruction and concluded that in general " _these sequences gave trees that were consistent with the well established phylogeny of the old world primates_ ".

* Divergent Patterns of Recent Retroviral Integrations in the Human and Chimpanzee Genomes: Probable Transmissions between Other Primates and Chimpanzees
* The decline of human endogenous retroviruses: extinction and survival
* Constructing primate phylogenies from ancient retrovirus sequences